This paper considers the problem of thermal shock in the case of a massive body in different conditions of heating and cooling. The most dangerous mode of heating was identified. The influence of inertial effects on the value of emerging thermal stress was investigated. A new equation of compatibility of stress with the inertial effects, which generalizes the known Beltrami-Mitchell relation for quasi-static cases, was obtained by methods of the tensor algebra. The theory of thermal shock in solids was developed in terms of dynamic problems of thermoelasticity in different forms of heat stress: temperature heating; thermal heating; heating medium. Equations for the calculation the jumps in the front of thermoelastic waves were obtained. The most dangerous mode of thermal shock was identified. The effect of relaxation in thermal problems was described in the context of the investigation of thermal stress state of a massive body. It was shown that an increase in relaxation time, i.e. heating rates of the boundary surface of the body, causes a reduction of thermal stress maxima. Original results of the thermal reaction of a solid to cooling were obtained. It was shown that, in comparison with the heating mode, the cooling mode is more devastating, especially for nearsurface layers of solids. The role of the relaxation temperature in the cooling mode was identified. New functional structures were proposed as analytical solutions to the major dynamic problems of thermomechanics on the basis of the use of the Kar functions, which are relatively new.