A system of equations is developed for the theory of bending of thick orthotropic elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate, i.e. ${omega}=0,;M_x=0,;M_{xy}=0;({omega}=0,;M_x=0,;M_{xy}=0)$ at simple supported edges. It can be obtained general solution that is added complementary solution ${omega}^e$ and paticular solution ${omega}^p$ by an assumption of solution function. In the next paper, this analytical results will be obtained for perforated thick plates.