Theoretical and numerical approaches were conducted in order to study supersonic exhaust diffusers to simulate high altitude performance of rockets on the ground. A physical model of concern includes a rocket motor, vacuum chamber, and diffuser, which have axisymmetric configurations. An analysis was conducted to investigate operation characteristics of supersonic exhaust diffusers from a flow-development point of view. Emphasis was placed on theoretical formulation to predict the starting pressure of diffusers, the effect of the vacuum chamber size, and the minimum starting pressure of the rocket motor to start the diffuser.