In this paper, for the first time, the modeling of Capacitance and sensitivity for MEMS capacitive pressure sensor with clamped square diaphragm is presented. In capacitive sensor the sensitivity is proportional to deflection and Capacitance changes with pressure. Therefore, first the diaphragm displacement, Capacitance and sensitivity of sensor with square diaphragm have been modeled and then simulated using finite element method (FEM). It can be seen that the analytical results agree with simulation. The results also show that the high sensitivity can be achieved by decreasing the diaphragm thickness and increasing its size.