Abstract: In view of severe vibration in the operational environment of ballistic missiles and rockets, the error propagation characteristics of the laser gyro strapdown inertial navigation system(SINS) in linear vibration environment were studied and it was noted that the square error of accelerator had a significant impact on the navigation accuracy. Then, a 31-order error model was established including the square error. In order to evaluate the accuracy of the model, the static and linear vibration simulations were designed to compare with the 28-order error model without considering the square error. The simulation results indicate that the two models have equivalent accuracy in the static state but the accuracy of 31-order error model is five times higher than the 28-order model in the vibration state.