A transient model for air-cooled, direct expansion cooling equipment was developed that runs faster than real time and handles the thermal and refrigerant flow transients associated with on/off compressor control. The model involves the solution of a set of first-order differential equations that arise from mass and energy conservation. The state variables include refrigerant pressures and enthalpies and temperatures of solid material. A novel method for handling the start up and shut down transients was developed. The model was validated using measurements for a 3-ton (10.6 kW) rooftop air conditioner.