This paper aims at proposing an elastically deformable surface with use of differential geometric structures. On the basis of the Theory of a Cosserat Surface, a computationally processable equation that relates the accumulated elastic energy and the variations in the differential geometry variables (metric and curvature tensors) of the deformable surface is presented. On the basis of our analysis, we propose a novel algorithm to compute more precisely, without compromising the interface's simplicity, the potential deformation energy in terms of the derivatives of the surface. With our proposal, we may maintain the finite difference scheme for computing deformations iteratively. Some simulation results are included.