Research "damp-off" a fungus disease that attacks the stem at and just below the soil level. It proliferates in excessively wet soil.

Compare photos of it with the appearance of your plants.

Dave

I planted the tomato plants around the beginning of May when the garden was still wet. I usually plant at this time and it has not been a problem. I also sprinkled some Milorganite around the plants as a organic fertilizer (new this year). According to one article on the internet, nitrogen encourages the fungi that cause damp-off. It seems that a combination of wet weather and Milorganite caused the problem. I will see how many more plants die, turn the soil over and add topsoil before planting any new tomato plants.