The paper presents problems of fatigue life prediction and technical state assessment on the example of chosen materials and components working under mechanical and thermal loading. The following problems have been discussed: methods of mechanical behaviour investigation of materials in specific operating conditions, modelling the object from the point of view of solids mechanics using FEM, relationship assessment between the structure of materials and their fatigue properties. Examples of equipment, used in the power, metallurgical and chemical industries were taken into consideration. The fatigue under mechanical and thermal loading testing methods has also been described. Results of fatigue tests of different materials have been shown and compared taking into account differences in mechanical behaviour of materials connected with their grade and structure.