SUMMARYThe problem of optimal design of the shape of a free or internal boundary of a body is formulated by assuming the boundary shape is described by a set of prescribed shape functions and a set of shape parameters. The Optimization procedure is reduced to determination of these parameters. For constant volume or material cost constraint, the optimality conditions are derived for the case of mean compliance design of elastic structures of a non-linear material. Some additional conditions for the global minimum of the mean compliance are proved. The most typical cases of boundary variations are discussed. The optimal shape problem is next formulated by means of the finite element method and the iterative solution algorithm is discussed by using the optimality criteria. Several simple numerical examples are included.