In this paper we propose a new approach for surface representation. Generative models are exploited for encoding the variations of local geometric properties of 3D shapes. Surfaces are locally modeled as a stochastic process which spans a neighborhood area through a set of circular geodesic pathways, captured by a modified version of a hidden Markov model (HMM), named multi-circular HMM (MC-HMM). The approach proposed consists of two main phases: 1) local geometric feature collection, and 2) MCHMM parameter estimation. The effectiveness of our proposal is demonstrated by several applicative scenarios, all using well-known benchmark datasets, such as multiple view registration, matching of deformable shapes, and object recognition on cluttered scenes. The results achieved are very promising and open up the use of generative models as geometric descriptors in an extensive range of applications.