Materials and their properties are at the core of engineering design.In many circumstances, materials behave linearly elastic, e.g. the deflection is linearly proportional to the applied force. However, at certain loads and other conditions almost all materials exhibit material response deviating from the linear elastic.This course will discuss different types of mechanical material behavior and present the corresponding material models and the numerical techniques for their implementation. In particular, the following material models will be considered: linear and non-linear elastic, elasto-plastic, visco-elastic, and quasi-brittle damage.