Why do my feet hurt after sitting for a while?

See below: It may be due to pressure behind the knee on the blood and nerve supply.

Plantar fasciitis: Plantar fasciitis, or an arch ligament strain is a very common reason for arch and heel pain in the bottom of the heel. There can sometimes be a bursitis under the heel as well. Other causes of heel pain can be tarsal tunnel syndrome, arthritis, a stress fracture, referred nerve pain among others. Talk to a podiatrist to help sort this out.

Possible: Plantar fascitis. The condition you describe is known as post static dyskinesia...Or pain after periods of rest and then standing. One explanation is that the ligament contracts while you are sitting and then stretches when you stand and this stretching of the ligament causes the pain.

Feet hurt: As Dr Kass said , that is a likely explanation. However , you did not state where the pain is. The right thing to do is get an evaluation to determine the cause