The boundary problem of plane stationary Stokes equation is changed into the variation equation which is equivalent to the boundary integral equations. With linear boundary elements, it is solved by Galerkin boundary element method. In computation of stiffness matrix, the exactly integral formula is used in the first integral expression. The numerical integral formula is used in the second integral expression. The authors deduce the analytical formula of the first integral in detail. The numerical experiments also prove this method is reliable and quickly. The error of Galerkin boundary method is tested with numerical experimentation.