In this paper, the method of initial functions (MIF) is used to solve the problem of bending an orthotropic plate clamped along all four sides, under the influence of a normal load uniformly distributed over its surface. The solution is obtained in the form of an exponential series with unknown coefficients. The algorithm of the method is such that on two opposite sides the boundary conditions (equality to zero of displacements and angles of rotation) are satisfied exactly, while on a pair of two other opposite sides the boundary conditions are satisfied with an arbitrary degree of accuracy by the collocation method. All studies were carried out using the Maple analytical computing system. This system allows you to perform calculations with an arbitrary mantissa in the representation of real numbers. Calculations with a long mantissa overcome one of the main disadvantages of the MIF: the computational instability of its algorithm, which arises under certain parameters of the problem. The computational stability of the obtained solution is investigated, as well as the stress-strain state in the neighbourhood of the corner points of the plate. It is shown that the moments and shear forces tend to zero when approaching the corners of the plate with a single change in sign.