This project is concerned with the study of laminar incompressible flows of viscous fluids. Both steady and unsteady flow problems have been investigated in this work. The flow regions consist of domains bounded by infinite parallel disks or plates - permeable or impermeable - or a fluid layer of finite thickness above a permeable region. Such flow problems have a number of engineering and industrial applications. In this project, we have discussed flow features of four specific problems: two steady flows and two non steady flows. In the Chapters 2 and 3, we have analyzed two steady flow problems from the literature. The first problem is concerned with a laminar source flow between tv disks. In the next problem, the extension of this source flow problem has been taken up by including the effect of rotation of bounding plates about a common axis. We have mainly focussed on obtaining the solution of the momentum equations. In both these problems, analytical solutions have been obtained using double perturbation series. The variation of the velocity components and wall shear stresses have been examined with regard to a number of non-dimensional parameters like Reynolds number due to the source term or the rotation, wall permeabilities, etc. In one of these problems, we have also used numerical method for comparison with analytical solution. The Chapters 4 and 5 deal with two types of unsteady oscillatory flows. One of the classical oscillatory flow problems, namely, the Stokes' second problem, has been re investigated in Chapter 4. The physical situation here corresponds to an oscillatory unbounded flow over an infinite rigid plate. We have extended this problem by considering the flow in a bounded domain. In the last Chapter 5, we have investigated a coupled viscous flow in a finite region consisting of a free fluid domain and a porous medium below it. Velocity distributions in both regions as well as the temperature in the free fluid region have been discussed.