Calculations for square rubber membranes comprise a complex two-dimensional problem of the physically and geometrically nonlinear zero-moment theory of thin shells. In an earlier paper, the method of nets was employed to solve the problem of inflation of a square membrane by a normal pressure. It was assumed that the material obeys Hooke's law. The same problem was dealth with in another paper, for a neo-Hooke material, within the confines of the ascending portion of the deflection at the center/pressure diagram. In this paper, to obtain a general solution of the problem we employ the nonlinear shell theory. To achieve reliable results, we employe two calculation methods, taking account of the essential nonlinearity of the problem, namely the finite-difference and variational methods.