A method based on the vorticity stream function formulation is used for the solution of the unsteady incompressible two-dimensional laminar viscous flow problems. Vorticity transport and stream function equations are written in generalized curvilinear non-orthogonal coordinate system, and discretized using an implicit finite difference approximation. A second order accurate scheme with a stabilizing correction splitting method as an ADI technique is used. Both conservative and non-conservative forms of the vorticity transport equation are considered and the problems associated with different treatments of boundary conditions are addressed. Several test cases, including rectangular cavity flow problem, flow around circular cylinder and flow past an isolated airfoil at moderate angles of attack, are illustrated.