This paper describes the development of a mechanistic thermo-hydraulic math model of the Pump Module Assembly (PMA) for use onboard Space Station Freedom. The PMA consists of the Rotary Fluid Management Device (RFMD), the Back Pressure Regulating Valve (BPRV), a bellows accumulator, and miscellaneous plumbing. The PMA components act to provide fluid pumping power, control system pressure, and control system fluid inventory. The Central Thermal Bus (CTB) is the primary method of transporting the waste energy generated by the station electrical loads from the acquisition point to final rejection to space. Since the CTB is a two-phase system, control of the operating pressure controls the operating temperature, and defines the heat rejection temperature of the station components. Accurate modeling of the dynamics of the PMA is critical to providing predictions of station thermal performance.Most current models of the PMA utilize an energy balance about the RFMD to define the required vapor flowrate to the condensing radiators. This method ignores the PMA thermo-hydraulics and therefore is applicable only for quasi-steady state conditions. The energy balance method is not capable of predicting PMA response for two important space station conditions; flooding of the RFMD due to rapid influx of ammonia and RFMD loss-of-subcooling due to inadequate heat rejection. The new model uses the mechanical operation of the PMA components to derive a mechanistic model capable of predicting most system responses. The new model considers the PMA thermo-hydraulics and accurately reflects system variables such as spring constants, flow areas, fluid conditions, and RFMD rotational velocities. This paper describes the PMA components and their operation, PMA models based on the energy balance approach, and the mechanistic PMA model. Transient responses are provided and compared to available experimental data.