Abstract We propose a new approach for template-based extensible surface reconstruction from a single view. We extend the method of isometric surface reconstruction and more recent work on conformal surface reconstruction. Our approach relies on the minimization of a proposed stretching energy formalized with respect to the Poisson ratio parameter of the surface. We derive a patch-based formulation of this stretching energy by assuming local linear elasticity. This formulation uni?es geometrical and mechanical constraints in a single energy term. We prevent local scale ambiguities by imposing a set of ?xed boundary 3D points. We experimentally prove the suf?ciency of this set of boundary points and demonstrate the effectiveness of our approach on different developable and non-developable surfaces with a wide range of extensibility.