The present study presents an analytical solution to the flow field of the unsteady laminar accelerated flow of a viscous incompressible fluid past an infinite vertical porous limiting surface, when the freestream is accelerated and the limiting surface temperature and concentration are given functions of time. The expressions for the velocity, temperature and skin friction are obtained by using Laplace transform, when the Prandtl and Schmidt numbers are given. Graphs showing variations of the velocity and the skin friction, for different values ofG r andG c (modified Grashof number), as well as of the temperature are plotted and the results are discussed.