Abstract This study develops a computational model of free-form shell generation in the design of roof structures that rely on the optimized behavior of the membrane theory of thin shells. For architects and engineers, the model offers a low cost, fast, and relatively easy design solution. A computational model for structural free-form shell generation is presented to simulate physical models of shell optimization. This method of designing optimized structures is based on mathematical programming combined with the finite element technique, and is inspired by the laws of nature and, in particular, by the Heinz Isler methods of designing shells using physical models. A flexible membrane is simulated automatically, initially in the horizontal plane surface, with any shape and boundary conditions, and able to carry several specified loads. The membrane under the action of these loads is deformed until reaching one of its equilibrium configurations, which defines the middle surface of the shell to be built. By the principle of minimum total potential energy, the positions of steady equilibrium of the membrane correspond to the local minimum points of the total potential energy function. When the total potential energy function does not exist, it is advisable to use an incremental Newton–Raphson-type method to find the solutions for the nonlinear system of equations given by the equilibrium equations of the membrane in the space. Structural analysis of thin concrete shells with the final shapes of the optimized membranes demonstrates which displacements and principal stresses are optimal. The computational method presented in this paper could be integrated, for example, with Contour Crafting (CC), a layered fabrication technology that offers the potential to construct full-scale buildings directly from three-dimensional computer-aided design models (3D CAD). Structural behavior is in accordance with the membrane theory of thin shells and aesthetic appeal is a natural consequence of the forms generated for applications in architectural design and civil engineering.