Using BEM to solve vibrating or unsteady Stokes flow is very attractive. At first we derive the Green functions for 2D and 3D. Then we deduce the relative formula, the explicit expression for pressure and the boundary integral equation. The integral equation is discretized into a set of linear algebric equations. In the case of 2D, the influence coefficients of the segment to itself are integrated analytically. In order to check such BEM, an example with analytical solution already exists is solved numerically. The result shows that the method based upon our Green functions is perfect.