The course provides a comprehensive overview od constitutive dependencies and constitutive models of matters, not only of solids (i.e. structural materials) but also of liquids and gases. It deals also with time dependence of stress-strain response of materials and describes it using different viscoelastic models. It applies the theory of finite strains of solids in description of non-linear elastic as well as non-elastic behaviour of elastomers and composites with elastomer matrix and of plastic behaviour of metals including their ductile fracture. It presents specific ways of material testing needed for identification of their models. For each of the presented models basic constitutive equations are formulated on the basis of which the response of the material under load is derived using both analytical and numerical (FEM) methods, including applications of the models in ANSYS software.