The thesis is concerned with the study of a particular class of micro-continuum fluids known as micropolar fluids. We present some of the aspects of the micropolar fluid theory and the equations of motion of these fluids. The first problem discusses the unsteady micropolar fluid flow between two parallel plates with zero pressure gradient assuming slip and spin boundary conditions. In the second problem, the unsteady motion of a micropolar fluid between two parallel plates with slip conditions for both velocity and microrotation under the effect of pressure gradient is discussed. Finally, we study the problem of an incompressible micropolar fluid flow outside an infinite circular cylinder with slip condition. In the considered problems, the solutions are obtained analytically in Laplace domain. The inverse transforms are obtained using a standard numerical technique and the results are discussed graphically.