The paper focuses on obtaining numerical results for a rectangular Reissner plate with clamped contour under the influence of a uniform load using the iteration superposition method of four types of trigonometric series (correcting functions). The initial function of bendings is selected as a quartic polynomial which turns into zero on the contour and is a specific solution to the main bending equation. Discrepancies in rotation angles from the initial polynomial are eliminated in turn on parallel edges by pairs of correcting functions of bendings and stresses which cause angular discrepancies themselves. During an infinite process of the superposition of these pairs, all discrepancies tend to zero, which gives a precise solution at the limit. The paper presents results of bending computations, bending moments, and shearing forces for square plates different thickness. The obtained results are compared with the results of other authors, as well as with Kirchhoff theory. It is shown that with the relative thicknesses less than 1/20, the results gained with both theories are almost the same.