A Computational Fluid Dynamics code was developed to study the flow characteristics of two dimensional laminar incompressible flow. Stream function-vorticity formulation was used for solving two dimensional continuity and momentum equations. The unsteady vorticity transport equation is solved by alternate direction implicit scheme. The stream function equation is solved by the successive over relaxation method. A computational code in c-language was developed to solve the tridiagonal system of algebraic equations. Two dimensional flow through a channel with rectangular block at the bottom wall was considered for the validation. The streamline patterns obtained for different Reynolds number shows good agreement with published results. The code was modified to simulate an incompressible laminar wall jet flow around a solid obstacle. Simulations were carried out for different Reynolds numbers. Contour plots of Stream line, u-velocity and v-velocity were obtained. The variations of flow patterns and the development of vortices were studied and reported.