3-RPS symmetrical parallel manipulator is the key part of the parallel supporting structure. By means of the complete differential-coefficient matrix theory, the mechanical position-stance error model expressed by Rodrigues Parameters including the main errors of the parallel supporting structure was established. The sensitivity percentage was proposed for describing the error sources of the parallel supporting structure, and the corresponding sensitivity model with statistical basis was achieved. According to the results of numerical simulation, the actuator errors and the errors of the moving platform along Z axis should be controlled strictly in the course of the design, manufacture and assembly of the manipulator. Although the structure scale was changed, the errors of high sensitivity should be considered fully. Based on the sensitivity analysis of the parallel supporting structure, the calibration is effective to reduce the errors of the kinematic parameters with high sensitivity.