An analytical solution is sought for the perturbation velocity field in a boundary layer with prescribed suction through a porous surface. Addressing the problem as an initial value problem, using stream- and spanwise Fourier transforms and Laplace transformation in time, yields solutions for the vertical velocity and the normal vorticity. Comparisons with the suction-free case are made and conclusions are drawn regarding the stabilizing effects of the suction motion. It is found that the analytical solutions give support to the theory that the presence of a porous boundary with suction acts stabilizing.