The steady, laminar flow of newtonian, incompressible, consant property fluid along porous-walled conduits is analysed for contions of variable suction or blowing through the duct walls. Both hydrodynamic and thermal problems are solved. Two geometries are assumed for the conduit: an open-ended straight circular cylindrical tube, and a flat duct formed by infinite parallel plates. Two kinds of thermal boundary conditions are adopted for both geometries: I – constant wall temperature and II – uniform conducton heat flow exchanged between the fluid and the internal sufarce. In all cases, it is determined the influence of the transversal mass flow over the momentum abda heat transfer coefficients. Several investigators have dedicated and increasing interest to these problems, due to their applications in engineering and medicine. Heat pipe multiple utilizations, as well as the search of obtainning more detailed information about fluid circulation in aniaml and plant organs, such as lung and arteries, are examples of such applications. The majority of published works about these problem makes use of a constant suction velocity as a hypotesis of work. Owing to a small amount of experimental data for comparison with theoretical results, may be questioned if it is an acceptable hypotesis. An investigation over the validity of uniform whitdrawal or injection is developed in the present work. The law of darcy for flow in porous media is introduced to give the wall velocity distribution and the results can be confronted with those for uniform suction or injection. The method used to solve the system of partial differential equations is based on power series expansion for the velocity and temperature. This technique does not impose a restriction on the applicability of the results in the sense of using similar velocity profiles or regions far from the entrance of the permeable pipe or channel. In both geometries studied, the velocity and temperature profiles are supposed as being fully devoloped at the duct entrance. The method is adequated only for moderate rates of suction or blowing, and for fluids with prandtl numbers of order of one, but can be extended, with some supplementary effort, to more general situations.