We propose an analysis method of an autostereoscopic display system with lenticular lens array using finite ray-tracing method that is verified by the geometrical optics. In the present work, we adopt the cylinder equation for the mathematical expression of the lenticular lens. For the calculation of the direction cosine of the transmitted ray, we first calculate the refracting point at bottom of the lens and the direction cosine of the incident ray that propagating through the lens by the Snell`s law, and then apply to finite ray-tracing method. Finally, we obtain the simulation results for the intensity distribution of the ray at optimal viewing distance. From these results, we confirm the realization of 3D image that exists separately according to the viewing position at an optimal viewing distance.