This paper shows how to compute the local second-order shape of an unknown surface with a force-controlled robot. Dedicated tools and paths are designed in order to make this shape recovery easier. Two basic methods are presented, based on measurements of contact forces and of positions and velocities of the end effector. The first method fits a surface through a set of contact points while the second method uses the shape of surface curves. Experiments show that following two curves of limited length is sufficient to identify second-order surface shape with an accuracy which is in general better than 10%. The most important result, however, is that this accuracy is sufficient to increase the performance of subsequent surface following tasks.