The study provides results of analytical research and computer simulation of an XY microscope stage with a piezoelectric actuator. It describes the operating principles of the XY microscope stage with parallel kinematics with bimorph piezoelectric actuators (BPA). We found the dependences of the displacement stage for the X and Y axes of the voltages applied to the BPA in quasi-static mode. We compiled equations of motion of the stage in two coordinates. Transfer functions of the displacement stage during controlling actions, i.e., voltage on BPA, are derived on the basis of equations of motion. We developed block diagrams of the control system with a PID controller for computer modeling in SIMULINK at stepping stepped exposure by the X and Y axes. Computer modeling has shown that with the introduction of the PID controller into the control system the dynamic system acts like an aperiodic link with sufficient speed positioning tasks.