The article is devoted to constructing fundamental solutions to the dynamic equations of a thin isotropic plate, which lies on Pasternak’s elastic foundation. The corresponding differential equations are obtained based on the classical small-deflection theory of thin plates. In solving applied problems, technical theory is the most widespread since it allows for the correct solutions for a wide class of real problems, such as thin plate theory. This model allows for the simplifying of mathematical formulations considerably and the carrying out of investigations by analytical methods. The method of fundamental solutions is an effective method for solving equations of the theory of plates in partial derivatives in the case of action on a body of static and dynamic loads of different natures. The constructed fundamental solutions are of independent interest as solutions to problems about the action on a plate. The presence of appropriate fundamental solutions makes it possible to significantly simplify the study of the response of a plate to local loads distributed over a certain area. The fundamental solutions are the basis for the method of boundary integral equations, which reduces the problem’s dimensionality by one and does not require discretization of the whole domain. This approach increases the efficiency of solving a whole class of applied problems in mechanics. The algorithm proposed in the work for constructing fundamental solutions of plate dynamics is based on the joint use of Fourier and Laplace integral transforms and the theory of special hypergeometric functions. The described technique can be easily extended to the case of material anisotropy, the construction of fundamental solutions to the theory of thin shells, and the case of considering some physical properties of the environment in the model.