In this paper, the order of convergence of finite difference methods& shooting method has been presented for the numerical solution of a two-point boundary value problem (BVP) with the second order difierential equations (ODE ’s) and analyzed. Suflicient condition guaranteeing a unique solution of the corresponding boundary value problem is also given. Numerical results are tabulated for typical numerical examples and compared with the shooting technique employing the classical Euler and fourth- order Runge-Kutta method using MATLAB 7.6. 0( R2008a).