In this article, the task is to consider the effect of the piston bending in an axial- piston pump under the action of hydraulic force on the kinematics of the pump. The change in kinematics due to the elastic deformation of the piston is estimated by the axial displacement of the piston face. The study takes into account the bias of the plunger in the gap, the elastic bending deformation of the plunger, the contact deformation of the plunger and the cylinder block. The task is considered on three models: a rigid piston in a rigid cylinder block; deformable piston in a rigid cylinder block; deformable piston, block, shoe, and disk. The values of the displacement of the piston, caused by elastic forces and misalignment in the gap depending on its position were obtained for the first time as a result of the analysis. The problem is solved both analytically and numerically using the finite element method. In the analytical solution of the problem, the piston is represented as a beam supported by pin and roller at the points of contact of the piston with the walls of the cylinder block. The three-dimensional model of the pump is applied to solve the problem by the finite element method, the contact deformation of the piston and the block is considered. According to the simulation results, the displacement of the piston is obtained depending on the position of the piston. The results of modeling an analytical model are presented in the form of a smooth function, and the results of numerical simulation using the finite-element method obtained for several points are interpolated by a smooth function. The conclusions suggest that the greatest deformations are achieved in the piston located at the bottom dead center, and the gap between the piston and the sleeve and the overall stiffness of the contact parts have the greatest effect. The results of the work can be used to correct the geometrical parameters of a heavily loaded aviation axial-plunger pump to reduce flow and pressure pulsations caused by the kinematics of the pump.