Abstract: Akin to the energy definition of thin-plate elastic deformation, ain this paper a complete energy model is established for deformable surface．The goal of establishing the energy model is to solve several key problems in surface modeling with B-spline．Different from traditional energy model, a in the proposed complete energy model, aboth the structural stiffness and physical meaning of design parameters are presented completely and clearly．The key techniques involved in this paper includes：1） describing deformable surface with configuration and displacement mode；2）deducing control equations based on the complete energy model；3）introducing finite element method to solve the control equation． The meshing technique using non-uniform B-spline elements made it convenient to deal with simply and clamped supported constraints．