A set of three nonlinear partial-differential equations is derived for general finite deformations of a thin membrane. The material that composes the membrane is assumed to be hyperelastic. Its mechanical property is represented by the neo-Hookean strain-energy function. The equations reduce to special cases known in the literature. A fast convergent algorithm is developed. The numerical solutions to the finite-difference approximation of the differential equations are computed iteratively with a trivial initial iterant. As an example, the problem of inflating a rectangular membrane with fixed edges by a uniform pressure applied on one side is presented. The solutions and their convergence are displayed and discussed.

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