If you're doing online research about undershirts, or clothes in general, you may come across something called undershirt pilling.  Like many of us, you may be unfamiliar with this term.  When clothes have been around for a while, you may notice small fabric clumps forming on them, especially after washing.
These give your clothes a worn-out look.  This effect is called pilling because the fibers form little "pills" all over the garment.  Normal wear and tear can cause weaker fabric fibers to break and get tangled up around stronger ones, forming those little clumps.
Some materials are more susceptible to pilling than others.  Cotton, wool, polyester, and other synthetics and synthetic blends are more likely to pill.  On the other hand, the chance of pilling is a lot lower with natural fiber (linen, silk, merino wool).  Here are some tips to prevent pilling so your undershirts and other clothes look better longer.
Before washing, turn the garment inside out.  This minimizes abrasion during laundering.
Sort garments before washing.  For clothes that are prone to pilling, launder them using your machine's "gentle" or "hand washing" cycle.  Avoid laundering lint-producing articles, like robes and towels, with other clothes.  Likewise, don't wash delicate and heavy-duty fabrics together.
Minimize the use of bleach and other harsh detergents.  Instead, opt for a detergent that contains cellulose.  This ingredient breaks down fabric pills so they fall off.
Use fabric softener in the rinse cycle.  Fabric softener coats fibers to protect them from abrasion and pilling.  If your machine has a fabric softener dispenser, you can pour the liquid in there and your machine will release it at the proper time.
Reduce use of the dryer, at least for delicate fabrics.  Hang these to dry if possible.  Otherwise, remove them from the dryer as soon as possible to prevent strands of other fabrics from attaching to them.
Don't overload the machine.  While we've probably all done this at some point, it leaves the clothes with less room to swirl around, making fabric fibers more likely to stick together.