The main attention is paid to a description of the principal computational methods for the solution of stationary boundary problems for both second order and fourth order elliptic equations. Nonlinear resolving equations are constructed, as a rule, by using finite difference methods and by variational difference methods. On the whole two-dimensional problems are discussed. One-dimensional examples are presented in order to explain the used approaches. The solution of concrete free boundary problems illustrates the possibilities of the computational methods discussed. In a separate chapter incorrect free boundary problems are outlined.