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This paper introduces a new stochastic surface model for deformable 3D surfaces and demonstrates its utility for the purpose of 3D sculpting. This is the problem of simple-to-use and intuitively interactive 3D free-form model building. A 3D surface is a sample of a Markov random field (MRF) defined on the vertices of a 3D mesh where MRF sites coincide with mesh vertices and the MRF cliques consist of subsets of sites. Each site has 3D coordinates (x,y,z) as random variables and is a member of one or more clique potentials which are functions of the vertices in a clique and describe stochastic dependencies among sites. Data, which is used to deform the surface can consist of, but is not limited to, an unorganized set of 3D points and is modeled by a conditional probability distribution given the 3D surface. A deformed surface is a MAP (maximum a posteriori probability) estimate of the joint distribution of the MRF surface model and the data. The generality and simplicity of the MRF model provides the ability to incorporate unlimited local and global deformation properties. Included in our development is the introduction of new data models, new anisotropic clique potentials, and cliques, which involve sites that are spatially far apart. Other applications of these models are possible, e.g., stereo reconstruction.