To provide a reliable theoretical basis for the selection, mounting, and error compensation of the polarization device in the synchronous phase-shift transverse shear interference system, based on the Jones matrix principle, we construct an error model reflecting the degree of influence of the errors of quarter-waveplate and polarizer array on the measurement results in the system. Then, we quantitatively analyze how the measurement results are influenced by the following factors: the phase delay error of quarter-waveplate, fast-axis azimuthal angle error, and transmission-axis azimuthal angle error of the polarizer array. The simulation results show that the wavefront measurement errors are 0.00002λ(PV) and 0.000062λ(RMS) when the phase delay error of the quarter-waveplate is within ±1°, 0.0001λ(PV) and 0.00006λ(RMS) when the adjustment accuracy of the quarter-waveplate is within ±2°, and 0.003λ(PV) and 0.001λ(RMS) when the azimuthal angle error of the polarizer array is within ±1°. According to the simulation results, the polarization components in the measurement system were selected. At the same time, two polarization components with different levels of accuracy were chosen for comparison experiments. The experimental results indicate the following conclusions: the deviations of the residual values of the experimental results from the residual values of the simulation results in terms of the PV and the RMS values are less than λ/20, and the validity of the model can be verified to a certain extent. The mathematical model proposed in this paper can provide a reliable theoretical basis for the selection of polarization devices in synchronous phase-shifted transverse shear interference systems.