The method of initial functions (MIF) is an analytical method used to obtain a solution of static and dynamic equations of the theory of elasticity. In three-dimensional Cartesian coordinates the method is effective for analysing thick plates (including layered ones) in case when loads on their two opposite faces can be expanded in trigonometric series. However for a thick plate its own weight mustn't be neglected. In the paper a partial solution of the inhomogeneous system of equations, which appear in the theory of elasticity, is founded and together with MIF is used to analyse a thick isotropic plate under its own weight.