Since 70s, the fixed-grid method of characteristics has been used successfully to analyze transient conditions in networks and pipeline systems. In analyzing transient flow, the use of an interpolation scheme is unavoidable, as the Courant number should be satisfied. Several interpolation schemes are introduced and used in solving water hammer classical equations. In this investigation, cubic-spline spatial-line interpolation scheme plus two new cubic-spline, time-line and combined interpolation schemes, are used to solve the approximate and complete water hammer eluations. All interpolation schemes are used to analyze transient flow in a pipeline containing three senes pipes with a reservoir and a valve. It is shown that for small time-steps, all interpolation schemes produce same results. For a large time-step, non-linear interpolation schemes perform better than the linear ones. The combined interpolation scheme used to solve the approximate equations has the best accuracy. In terms of accuracy and computational time, the cubic-spline time-line interpolation performs the best for both approximate and complete water hammer equation