In Micro-electro-mechanical Systems (MEMS) based pressure sensors and acoustic devices, deflection of a membrane is utilized for pressure or sound measurements. Due to advantages of capacitive pressure sensor over piezoresistive pressure sensors (low power consumption, less sensitive to temperature drift, higher dynamic range, high sensitivity), capacitive pressure sensors are the 2nd largest useable MEMS-based sensor after piezoresistive pressure sensors. We present a normal capacitive pressure sensor, for continuous sensing of normal and abnormal Intraocular Pressure (IOP). The composite membrane of the sensor is made of three materials, i.e., Si, SiO2 and Si3N4. The membrane deflection, capacitance variation, mechanical sensitivity, capacitive sensitivity and non-linearity are discussed in this work. Mathematical modeling is performed for analytical simulation, which is also compared with Finite Element Method (FEM) simulations. MATLAB is used for analytical simulations and CoventorWare is used for FEM simulations. The variation in analytical result of deflection in membrane w.r.t. FEM result is about 7.19%, and for capacitance, the variation is about 2.7% at maximum pressure of 8 kPa. The non-linearity is about 4.2492% for the proposed sensor for fabrication using surface micro-machining process.