The authors investigated finite element (FE) analysis of damped modal vibrations in complex geometries of micro-electromechanical (MEM) resonators. Q-factor values were determined by taking the thermo-elastic damping into account. The basic model created is presented as a system of partial differential equations, which describe the elastic and thermal phenomena in the MEM structure. Mathematically the problem is formulated as a complex eigenvalue problem. Modal properties of square- and ring-shaped bulk-mode MEM resonators were investigated by taking into account the layered structure of the MEM system and the influence of the geometry of the clamping zone. The calculations were performed by employing the COMSOL Multiphysics FE software. The solution method was verified by comparing numerically and analytically obtained damped modal properties of a MEM cantilever resonator.