A practical numerical model for liquid crystal cell is set up based on the geometry structure of liquid crystal optical phased arrays (LCOPA). Model parameters include width and space of electrodes, thickness of liquid crystal layer, alignment layers, electrodes and glass substrates, pre-tilted angles, dielectric constants, elastic constants, the refractive indexes and so on. Especially, the thickness of alignment layer is first considered to the best of our knowledge. According to electrostatic field theory and Frank-Oseen elastic continuum theory, two dimension (2D) electric potential distribution and 2D director distribution are calculated by means of the finite difference method on non-uniform grids. And the phase delay of LCOPA is derived from crystal optics. The influence of cell sizes on phase delay distribution is analyzed. The evaluation function of fringing field effect is provided. And the methods to decrease fringing field effect between electrodes are also discussed.