The article considers the calculation of the flow of a viscous incompressible fluid in piston seals of piston hybrid power machines. The most widely used and effective seals are considered: a smooth gap seal and a step-type gap seal, and—based on the references analyses—the initial boundary conditions for their calculation are determined. The laminar and turbulent flows in gap seals are calculated based on the well-known analytical relationships, experimental studies and flow models, including the k-ε, Menter’s Shear StressTransport (SST) and Reynolds Stress (RSM) turbulence models. The effectiveness of using each model to determine average velocities, flow rates, and velocity plots in the cross section of a gap seal, as well as the adequacy of the description of known physical laws, is estimated. The results proved that the RSM turbulence model is better for the gap seals of different types under different modes of motion.