This paper presents a new method for projecting a mesh model of a source object onto a surface of an arbitrary target object. A deformable model, called Self-organizing Deformable Model(SDM), is deformed so that the shape of the model is fitted to the target object. We introduce an idea of combining a competitive learning and an energy minimization into the SDM deformation. Our method is a powerful tool in the areas of computer vision and computer graphics. For example, it enables to map mesh models onto various kinds of target surfaces like other methods for a surface parameterization, which have focused on specified target surface. Also the SDM can reconstruct shapes of target objects like general deformable models.