An inflatable sport ball, such as a basketball, a football, a soccer ball, a volleyball or a playground ball, is provided with a self-contained inflation mechanism, or multiple self-contained inflation mechanisms, for inflating or adding pressure to the ball. The mechanism is a pump which is retained inside of the ball and which is operable from outside of the ball to pump ambient air into the ball. The pump additionally contains an integral pressure relief device to selectively relieve the pressure of the ball. Instead or in addition to the pressure relief device, the pump optionally contains a pressure indicating device to determine the relative pressure of the ball. The pressure indicator provides a numerical indication of the internal pressure of the ball as measured or determined by a pressure sensor.