The Side-by-Side (SBS) Hybrid is one of several Revolutionary Vertical Lift Technology (RVLT) concept aircraft identified by NASA to investigate Urban Air Mobility (UAM) requirements. This paper presents a dynamic model of the SBS Hybrid powertrain built using the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS) and the Electrical Modeling and Thermal Analysis Toolbox (EMTAT). The model consists of the rotors, electrical power system, and turboshaft engines connected through freewheeling clutches, gearboxes, and multiple shafts. This research effort models the complex behavior of the powertrain, including the operation of the freewheeling clutches and electrical power system at the simulation time scale of the shaft dynamics. Several simulations highlight the key features present in the model and demonstrate its operation.