The fluctuation of free surface water in surge tanks is of great interest for its design. For this, various mathematical models exist for the analysis of mass oscillations in a surge shaft following valve adjustment. This paper describes a finite element technique using weighted residuals method for the solution of the governing differential equations. Three weighting functions are applied and the results are compared with those from classical methods. First, a relatively simple case of surge analysis with a sudden load rejection in the penstock is analyzed but neglecting tunnel friction. Then friction is included for test and comparison. The results indicate that the proposed numerical approach leads to an accurate simulation of the water surface motion.