The technical rerm for pee shyness is parauresis. It is a specific social phobia and it's been somewhat of a problem much of my life. In my case it was self-reinforcing because I felt embarassed about being pee shy. I was usually fine if there was a partition between urinals but practically rubbing shoulders with the next guy would cause me to tense up. I made some headway by doing arithmetic in my head, as others here have posted. Then about a year ago i observed a demonstration of a procedure called Emotional Freedom Technique (EFT). It sounds kind of crazy because you tap yourself on the face and chest in specific patterns while saying or thinking a specifc counterphobic message.
The demonstration involved someone who had a phobia of airplanes. Just talking about it caused this person to start sweating. The person presenting offered the audience that we could do this at the same time so I did, tapping and repeatedly saying to myself "No more pee shyness."
Well, at the end of the five minute exercise, the person with the airplane phobia reported feeling much calmer and was no longer sweating. As the months went by, I began to find peeing at urinals without partitions next to another guy to become easier. Most recently, I was at my gym and went to pee. As I came around the corner I noticed a big muscular guy was already at the other urinal. I briefly considered going to a stall but said "Fuck it" to myself and went to the urinal. I had no trouble starting or finishing and am feeling pretty pleased about this.
So... for guys who are dealing with this, you might want to look EFT up on the internet. There are said to be quite a few sites.
Dave