The thermomechanical modelling method is becoming an important tool nowadays for the refractory researchers, suppliers and end-users. On one hand, applications focus on the post-mortem thermomechanical analysis to interpret the occurred failure phenomena of refractories in service. On the other hand, a priori investigation is very helpful for the design of refractory lining concepts before putting them into effect; as a result it will minimize the probability of refractory lining premature failure and save costs for the refractory suppliers as well as for the end-users. For both investigation routines, suitable material constitutive models and testing approaches are of relevance. Existing material constitutive models often used for refractories are the fictitious crack model acting for tensile failure, the Mohr-Coulomb or Drucker-Prager model describing shear failure, and the Norton-Bailey model representing creep. To characterize the tensile and shear failure of refractories at room temperature and elevated temperatures, a wedge splitting test and a modified shear test can be applied, respectively. The creep behavior and corresponding creep parameters of refractories can be determined with an appropriate creep testing device at elevated loads. The proper application of material constitutive models and testing approaches allows for improving the thermo-mechanical modelling and the optimization of the lining design.