In general, mesh smoothing is performed by minimizing the discrete energy function for the surface. One of the major problems in mesh smoothing is to prevent the mesh from shrinking. In this paper, we propose a novel volume constraint to address the shrinking problem in mesh smoothing. Our key observation is that the mesh can be efficiently smoothed patch by patch in a signal processing manner, and then a local volume preserving constraint can be easily imposed to the energy minimization problem associated with the small patch, called the smoothing stencil, so as to effectively avoid the mesh shrinkage. In our implementation, the smoothing stencil is the 1-ring neighboring region of an edge or a triangle. And the constrained minimization problem is solved by a 2-step approximation method for efficiency. A series of examples demonstrate that the proposed smoothing method can be applied to remove noise from a mesh or remove rough detail from an original mesh to generate a smooth model in object reconstruction and geometry modeling. c 2002 Elsevier Science (USA)