Abstract: In this talk, we shall introduce the governing equations and numerical methods for the vesicle problem. A vesicle membrane surface is known to be incompressible and exhibits bending resistance. Instead of keeping the vesicle locally incompressible, we introduce a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension (Lagrange multiplier for the incompressible constraint) can be avoided. Nevertheless, the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension. Meanwhile, we will also introduce a linearly semi-implicit scheme that solves the velocity, pressure and tension altogether. The newly developed scheme can be proven to be unconditionally energy stable.  A series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method.