In this chapter, we presented new approaches for monocular reconstruction of inextensible surfaces imaged by a perspective camera. In particular, we proposed a SOCP formulation of the problem that accounts for noise in both the template and the input images. We also designed an algorithm that directly reconstruct a smooth surface based on free-form deformations. This algorithm outperforms previous approaches in terms of precision of the reconstructed surface. Besides, we experimentally showed that the surfaces reconstructed with this algorithm are truly inextensible. The only drawback of this approach is that it is formulated as a non-linear least-squares minimization problem with a non-convex cost function. However, we proposed a method to build an initial solution which is close to the optimum. It allows us to get rid of the difficulties linked to the non-convexity of the cost function.