Using the modified Hooke's law equation that takes into account the relaxation of stresses and strains, we have obtained the relaxed thermal dynamic stresses equation that includes summands subject to the relaxation properties of materials. An exact analytical solution to a heat conductivity equation derived with the local nonequilibrium of the thermal process in mind was used as a temperature function. An analysis of the exact analytical solution to the thermal dynamic stresses equation for an infinite plate with outer surfaces affected by heat impact indicated the elimination of the abrupt stress variation caused by solutions to classic equations, which do not take into account the relaxation properties of materials. The analysis also showed that in each point of the plate, stresses change following the harmonic law with an oscillation amplitude damped in time. Displacement changes also follow the harmonic law and result in high-frequency harmonic oscillations due to the periodic compression and expansion of the plate in relation to the centre of its thermal symmetry. (C) 2019 Elsevier Ltd. All rights reserved.