There's definitely an aspect of mental strength to it.  The only thing I really do to train myself for the race is to not listen to music on quality days or long run days.  It's not a big thing, but it does show me that I can be in my own head for a long time, and that I can rely on myself when I'm hurting.

There's also the much discussed "mantra" to consider.  This isn't really something I go to, but I found that I developed one mid-race in my last marathon.  "Win this mile" seemed to be working for me, and it helped me focus on not getting ahead of myself and just meeting my pace for each individual mile.

Lastly, I do think there's a huge difference between mental strength from my first marathon compared to others.  Even though I ran a decent time in my first, I walked for a little bit.  There was no physical need to walk, but mentally I didn't understand what my body would feel like and what kind of discomfort I could tolerate.  Unfortunately, I think experience is the best teacher in this regard and I don't think there's any way to really speed up the learning curve.

I think it can be hard to separate the physical vs. mental side of it. Better training & doing so over a long period of time (i.e. years rather than months) helps both. The stronger you are physically, the less you should need the mental side & vice versa. And of course starting at the proper (slow enough) pace should help you at the finish.

I have only run 2, both times I wanted to stop after ~mile 20 with every fiber of my being. In the first it was due to severe muscle/joint pain/stiffness; I did actually take a few walk breaks through the aid stations. In the second it was sheer fatigue, but I forced myself not to take any walk breaks. Despite the fact that I was better trained, it was not any easier mentally (OK maybe I am now contradicting myself, or maybe I just remember the 2nd one better because it was a month ago). For nearly the last hour, all I could think of at every moment was how badly I wanted to stop & walk. (Even at Mile 26! I had no glorious sprint to the finish, totally gassed.) So now that I am thinking this through, and the more experienced marathoners may validate this - the mental part will always be huge, since better training will cause you to push yourself that much harder.

I never run with music, not sure whether than makes a difference or not.

The only preparation I can think of is the training runs where you so badly want to cut it short, but you push through it & finish anyway.

And I think just the amount of time & energy you put into training helps - during the toughest parts of the race, you will keep reminding yourself how hard you worked for this and how much you want make the best of it.

To me, marathons are 90% mental. 

Figuratively speaking yes, literally, it's probably closer to 90% training, but I know what you mean.  It's an idiom that's used often and rightly so.

I have run two, one with music and one without, and for me, music is a moot point.  You are either in marathon shape (physically) or you are not.  Mental strength may pull you through the darkness of the late miles, but it is not going to make up for insufficient training.

Assuming you are in marathon shape, visualizing the course at different mile points during training runs will give you a familiarity that may help you through rough patches on race day.

You sometimes hear people say they could see the finish line in their heads and it helped them pull through late in the race, that may not be the case for everyone, but if you can channel your inner bad ass and get over the hump, then by all means, channel!

Ninety percent of  the marathon is half mental.

Thanks for everyone's input. At one time I ran w/music during training runs but I have not for about 6 months.  Regarding visualizing the course is a good suggestion.   I plan to research online the course, view videos of the course, and perhaps incorporate these visuals during my long runs.

Not quitting on a "bad" training run is another good suggestion.  I can foresee mentally telling myself if I quit during a training run what would prevent me from quitting during the marathon at a difficult juncture.

I'll keep all these ideas in my mind since I will run the marathon without a running buddy however two siblings and some former neighbors plan cheer me at different vantage points of the Richmond Marathon.

Agree completely with lily that you build mental toughness in training just as you build physical toughness.  It's also good to read a lot so you know what to expect.  One of the best things I ever read about the marathon came from Pete Pfitizinger.  He said that you keep hoping that all of your 20+ mile long runs and your 12-15 mile marathon pace runs and all of your other training will make it hurt less after Mile 20 and it never does.

In my first marathon, I reached Mile 18 relatively comfortable.  By the time I was somewhere between Mile 19 and Mile 20, it started to feel like someone was sticking knives into each calf with every stride.  At Mile 21, I added baseball bats to the quads.  Every step was a new experience in pain.  That's when I started passing people.  This was a small race so I didn't pass a lot of people but I passed 10-15 and not a single person passed me.  You will never convince me that I was in better shape than all of those folks.  Sure, I was in better shape than some who had simply tried to run beyond their ability but I think others didn't realize that the pain they were enduring was normal at that point in the race.  I will say that even I didn't expect it to be as bad as it was and it was horrible.  I mean really, really bad.  But, my pace for that final 6.2 miles was the same as my pace for the first 20.  Rather than crawling in because I was hurting, I knew that what I was feeling was no different than what Olympic caliber runners feel during an all out marathon.

Mind you, I have also run a marathon without going all out and I got a bit stiff and sore but it didn't hurt anything like my two all out marathons have hurt.

Reading a lot can also help prevent you from doing stupid stuff like going out too fast.  How?  Just by reading race reports from people who blew up and walked the last few miles.  You don't have to repeat their mistakes.

I found that training through anything and everything really changed my definition of hard. -5 degrees, snowing sideways, and wind? Go run. 90 degrees with 87% humidity and no breeze? Go run. Legs dead, working overtime, and feeling stressed to the max? Still go run. I'm not saying I never missed a run but I ran a lot of days that I absolutely would have skipped before. And I've done a lot of workouts that I would have said were too hard before. If my plan says to do something now I pretty much find a way at all costs, even rearranging days or taking vacation from work. I don't ever want to race another marathon (7 so far) with a single doubt in my mind that I could have trained better.