In this work, we describe the development and implementation of a hybrid finite element based  software “μsys” for the analysis of coupled multi-physical phenomena encountered in Micro-Electro-Mechanical Systems (MEMS) or microsystems. The developed computational strategy entails the use of  hybrid finite elements for modeling structures, which overcomes some of the inherent shortcomings associated with the interpolation incompatibility of the finite elements. As a result, a coarse mesh with a single type of high aspect ratio element can be used for computationally efficient solution of many kinds of coupled partial differential equations. The same element is used to interpolate multiple state variables including displacement, temperature, fluid pressure and electric potential etc. Additionally, we use direct, rather than staggered, approach to solve coupled PDEs.  The μsys software has modular architecture to seamlessly interface the analysis codes with various packages having pre and post-processing capabilities. This helps the user to work with familiar and accessible pre- and post-processing environments while using μsys as the versatile  finite element analysis engine. We illustrate the architecture and working of μsys with two coupled analysis modules, viz., coupled structure-electrostatics and coupled structure-squeeze film.  Pre- and post-processing capabilities of a commercial finite element software are used to demonstrate working with  μsys   as an example.