Why do people feel sleepy after overeating?

Several reasons: The part of the nervous system called the parasympathetic system kicks in. Blood goes from the brain and muscles to the gastrointestinal track to help digest the food. Hormones like Insulin kick in so the body stores fat. A person feels like a nap in order to better allow the entire process to take place amplified by the conversion of chemicals in food which act on the brain causing tiredness.