We consider the influence of withdrawal or injection of a fluid through a porous surface on the flow limited by a long parallel slider. Due to the no-slip conditions, the flow lacks of symmetry. But, a choice for a vertical velocity independent on the gap between the two surfaces is equivalent to a classical similarity solution. Then, the governing equations are reduced to a set of three ordinary differential equations. The quasilinearization method is a powerful tool to resolve these equations as soon as a first approximate solution is known. In both cases of small and large values for Re, we present an asymptotic formulation and use these first solutions for the scheme. A comparison with our numerical results shows that, respectively, these two approximations can be used until Re<5 for the first one and if Re>25 for the second. The different numerical results (velocity profiles, pressure, lift and drag) as functions of Re are analysed and compared with other published values.