A computational model of rectangular reciprocating seals, previously developed for elastomeric seals, has been extended to cover the mechanics and elastohydrodynamics (EHD) of composite seals comprising two polytetrafluoroethylene (PTFE) and one central elastomeric part, chemically bonded together. The model is demonstrated on a rotary vane actuator application and shown to produce realistic results regarding the contact pressure, film thickness, leakage, hydrodynamic friction force, and seal extrusion. Total computational time is very short, typically up to five hundredths of a second (0.05 s) on a 1.5 GHz personal computer. The main purpose of the model is the analysis and optimisation of said composite seal such that it outperforms the elastomeric seal (of exactly the same dimensions) in terms of leakage, hydro-dynamic friction, and extrusion in a wide range of operating conditions. For this goal, the PTFE-to-seal volume ratio of the composite seal is initially varied between zero and 90 per cent, and the results on leakage, hydrodynamic friction force, average film thickness in the sealing contact, and extrusion length of the composite seal are plotted and compared with those of the elastomeric seal for nominal operating conditions at three temperatures (−54, +22, and +99 °C) and for both flooded and starved lubricating conditions in order to find a first approximant to the optimum PTFE-to-seal volume ratio that gives the composite seal better overall sealing performance. Then, using the selected approximant of the optimum ratio, a parametric study is performed to compute the effects of seal interference (proportional to contact pressure), contact velocity, seal corner radius, and degree of lubricant starvation of the sealing contact on leakage, friction, and seal extrusion at the previously mentioned three temperatures for both flooded and starved contacts, thus establishing the regions of operating conditions and design parameters that benefit one seal or the other. It was found that, overall, the composite seal, despite a small (insignificant) disadvantage on leakage, significantly outperformed the elastomeric seal in terms of hydrodynamic friction and extrusion. Further optimization is possible, depending on performance priorities (for example, if leakage is valued more than friction, or wear more than leakage, etc.).