A finite difference scheme comprising of two step Lax-Wendroff and Leap-frog techniques used to solve the continuity and momentum equations for a fuel injection system, is described in this paper in addition to the method of characteristics. Newton-Raphson method and Becchi's techniques have been tried to solve the boundary condition equations. A limited comparison with the well known Runge-Kutta scheme showed that the Newton-Raphson method is much simpler to apply and needs lass computational time. The validation of the above model has been carried out by comparing the predicted and experimental data of the fuel injection pressures and rates. This comparison showed that the present model could be utilized to predict the performance of the injection system with a reasonable degree of accuracy.