The main approaches to building mathematical models of a continuous medium based on modern representations of the thermodynamics of irreversible processes are presented. The main attention is paid to consideration of generality of construction of models of thermoelastic continuous media, linear fluid, thermo-viscoelastic and thermoplastic media based on ideas about continuous media of velocity type, media with internal state parameters and media with memory. For scientists, engineers, graduate students and senior students of technical universities specializing in the field of continuum mechanics and mathematical modeling.