This paper presents a geodesic-based constrained deformation method for polygonal mesh models. After a user specifies a series of constraints (which may consist of points, lines and faces), their effective radii, maximum displacements, scaling, and rotation angles, the method creates the deformation weights for the vertices of the mesh surfaces using the field values determined by the geodesic distances between the vertices and the constraint sources. Compared with the traditional constrained deformation model based on Euclidean distance, this method can avoid the undesired deformation on the regions near the constraints. Experimental results show that the new deformation model is both efficient and intuitive.