Non-linearities play an important role in micro- and nano-electromechanical system (MEMS and NEMS) design. In common electrostatic and magnetic actuators, the forces and voltages can depend in a non-linear way on position, charge, current and magnetic flux. Mechanical spring structures can cause additional non-linearities via material, geometrical and contact effects. For the design and operation of non-linear MEMS devices it is essential to be able to model and simulate such non-linearities. However, when there are many degrees of freedom, it becomes difficult to find all equilibrium solutions of the non-linear equations and to determine their stability. In this paper a generic methodology to analyze MEMS devices using path following methods is described. Starting from the energy and work expressions of electromechanical systems (Section 1), the equations of motion, the equilibrium and stability conditions are derived (Sections 2, 3 and 4). The basics of path following are introduced in Section 4. Using several examples it is discussed how path following can be implemented in Mathematica, Matcont and in the FEM package Comsol (Sections 5–8).