In this paper the phenomenon namely fingering which occurs in the flow problems of oil reservoir engineering has been discussed. The effects arises due to the fingering have been studied by using the Darcy’s law together with different kinds of suitable assumptions and conditions. The problem is then modeled into mathematical form which yields second order partial differential equation. The equation is then solved by using singular perturbation technique together with initial and boundary conditions. The solution is then interpreted in terms of fluid flow terms.