A spectral inversion model of solid Mach-Zehnder imaging spectrometry is derived strictly. Based on the model, the influences of the reflector translation error on the spectral inversion are analyzed. Zemax software is used to establish the simulation model of the imaging spectrometry. The simulation model is then adopted to simulate the function of solid Mach-Zehnder imaging spectrometry and verify the validity of the theoretical derivation. Both theoretical analyses and simulation results indicate that the reflector translation error of solid Mach-Zehnder imaging spectrometry influences the spectral inversion, and the spectral inversion error relates to the sum of the reflector translation errors in the two shearing light paths. Therefore, it is necessary to strictly control the sum of two translation errors or compensate the measurement errors properly to improve the spectral accuracy of the measurement system.