An analytical method is presented that provides a better approximation for design parameter values of a MEMS capacitive microphone. The spring softening effect associated with the nonlinear characteristics of the electrostatic pressure due to a bias voltage, and the spring hardening effect associated with nonlinear stretching of the central region of a uniformly loaded fully clamped diaphragm with residual stress are both considered. The method allows a more accurate determination of the developed electrostatic pressure, maximum diaphragm deflection and the pull-in voltage. The resulting electrostatic pressure, pull-in voltage and deflection profile of the diaphragm are in close agreement with finite element analysis results.