Abstract: In this talk, we introduce an immersed boundary scheme to solve the non-stationary Stokes equations for inextensible interface problems with bending. The problem comes from the simulations of the vesicle dynamics in fluid flows. The scheme uses a linearly semi-implicit discretization for the non-stationary Stokes part and we have proved that the spreading operator acting on the tension and the surface divergence operator acting on the velocity are skew-adjoint  both mathematically and numerically so that the resultant matrix without bending is symmetric.  Based on the scheme, we can successfully estimate the local error of the stretching factor.  Moreover, we can prove that the proposed immersed boundary scheme is unconditionally energy stable.