In the lecture we first talk about the modeling of mechanical systems and the required idealizations. Then we continue with a brief summery of the kinematics and dynamics of multibody systems and show that after linearization the structure of the resulting equations is very similar to the one known from FEM. In the second part we focus on optimization problems and talk about all necessary steps from the problem statement to its numerical solution. Import topics are the multicriteria optimization, the sensitivity analysis as well as deterministic and stochastic optimization algorithms without and with constraints. The lecture is accompanied by exercises and computer demonstrations