[en] Numerical method for solving three-dimensional stellar structure problems, formulated as free boundary problems for a mildly nonlinear elliptic partial differential equation, is developed by a combination of Newton-Raphson procedure, trial free boundary method, a pseudospectral Galerkin type method (for angular dependence) and finite differences (for radial dependence). Implementation of the method on a computer is discussed. The method is applied to the computation of structure of a critical, polytropic primary in a synchronous binary system. For n = 3.0, the results are found to be in reasonable agreement with those obtained previously by an expansion method. This expansion method is not capable of computing the structure of the other interesting polytrope with n = 1.5 which presented no difficulties to the present method. (Auth.)