This thesis has two principal objectives. Firstly, to obtain exact solutions for some non-Newtonian fluids of rate and differential type including second grade fluids, generalized Oldroyd-B fluids, Burgers’ fluids, and generalized Burgers’ fluids. Secondly, to study the magnetohydrodynamic (MHD) and porosity effects on such fluids. More precisely, the basic aim is to find the velocity field and the shear stresses corresponding to the unsteady motion of rate and differential type fluids through porous media in different situations in the presence of magnetic field. The flows induced by oscillating shear stress and oscillating velocity on the boundary have been studied. The partial differential equations obtained from the mathematical formulation of these problems have been solved using analytic techniques, i.e., the Laplace transform, Fourier transform, and Hankel transform. The obtained solutions satisfy all the imposed initial and boundary conditions. The similar solutions for some simpler non-Newtonian and Newtonian fluids, have been obtained as limiting cases of general solutions. By means of graphical illustrations, the influence of magnetic and porosity parameters, effect of various parameters on the steady-state and transient velocity contributions have been presented and discussed.