A method of structural synthesis is proposed to set disposed shape of a flexible frame within an allowable region. Members of the flexible frame, which are initially straight, are discretized into straight bar segments linked by virtual coil springs at nodes. Assuming total strain energy is independently separated into two contributions of bending deformation by the springs and rectilinear deformation by the segments, we find positions of the nodes in the disposed state by means of the Lagrange multiplier method that searches for a stationary point of the total strain energy under the constraints on geometrical boundry conditions. A new formulation of the sensitivity analysis is derived to approximate the change of the found nodal positions with respect to design variables in the first-order sense. A layout constraint to exclude all the nodes from convex prohibited regions in disposed state yields governing equation of design variables in the form of linear simultaneous equations with rectangular matrix of coefficients, which is dealt with by the Moore-Penrose generalized inverse. A numerical example concerning with Y-shaped frame whose disposed shape is constrained by three prohibited regions demonstrates the validity of the proposed formulation.