Distance function induced by a surface is known to carry a great deal of topological information about the surface and its embedding in space. It is a natural question whether similar information can be extracted from the distance function induced by a dense discrete sample of the surface. In this talk we introduce a systematic approach to this question based on "distance flow" which is a flow maps that results from integration of a vector fields that generalizes the gradient of the distance function induced by a discrete point-set. The continuity of this flow map provides a natural way for determining the homotopy type of the sampled surface and its medial axis. In particular, this approach results simple and natural algorithms for reconstruction of surface and its medial axis. Moreover, the well-known WRAP reconstruction algorithm of Edelsbrunner can also be analyzed in this framework.