Bulging veins during exercise are a normal result of the increase in arterial blood pressure that occurs during exercise, explains Scientific American. The bulging is neither a good sign nor a sign of a dangerous condition.
When arterial blood pressure increases during exercise, plasma in the capillaries is forced into the tissue surrounding the muscles, and this is what causes the hardening of the muscles that's apparent during exercise. Because the muscles swell in response to the action of the capillaries, the veins nearest the skin's surface are pushed toward the skin. People with less subcutaneous fat are more likely to notice this phenomenon as bulging veins, according to Scientific American.