The unsteady flow of a dusty viscous incompressible fluid through porous medium in a long rectangular channel under the influence of time dependent pressure gradient has been studied. The solution of governing equations of motion is obtained by the application of Finite Fourier cosine transform and Laplace transform to study the behaviour of the flow of fluid and the dust particles through porous medium. The particular cases when the pressure gradient is (i) an absolute constant,
(ii) periodic function of time, (iii) an exponentially decreasing function of time and (iv) Ctet , have been discussed in detail.