This paper presents the design procedure for thorough analysis of a closed loop Micro-Electro-Mechanical Systems (MEMS) capacitive accelerometer system based on sigma-delta modulation technique. A signal conditioning IC has been designed in UMC 180 nm process in Cadence Analog Design Environment. To perform detailed simulation of the entire system, the MEMS device has also been replaced by its electrical equivalent model on the same platform. Since the closed loop system may suffer from stability issue, a lead compensator design with proper coefficients has also been discussed. The procedure can be followed for the design and analysis of different types of closed loop MEMS capacitive accelerometers.