In our paper, we study a traveling wave in a transversely isotropic medium caused by the resulting temperature gradient between layers during 3D printing of building structures. To describe this process, we use a three-dimensional model defined by a system of first-order differential equations, which, in addition to the components of the displacement vector and temperature, contains additional functions. Formulas are obtained that express the components of the displacement vector and temperature through the wave parameter. This made it possible to obtain the dependence of the displacement vector on the temperature in the traveling wave. As an example, for specific values of the quantities on which the traveling wave depends, we plotted the dependence of the components of the displacement vector on temperature.