The paper deals with finite element analysis of damped modal vibrations Q-factor values determined by thermal-elastic damping in micro-electrical-mechanical systems (MEMS). Mathematically the problem is formulated as a complex eigenvalue problem. Verification problems have been solved by using several computational environments and different presentations of model equations in order to comprehend and reduce the influence of rounding errors. The analysis of damped modal properties of selected real MEMS resonator revealed the main features of thermal-elastic damping by taking into account 3D geometry of the resonator and anchoring (clamping) structure.