The finite-difference methods of Lax, Lax-Wendroff (two-step), and the donor celt type, and the finite-element method using a Galerkin procedure with B-splines as approximating functions are compared with the method of characteristics for the solution of waterhammer transients as typified by valve closure problems. From the point of view of accuracy, the two-step Lax-Wendroff method and the method of characteristics are comparable and produce the best results. The Lax method fares worst. The donor cell type and the Galerkin procedure with quadratic B-sptine basis as approximating functions display roughly the same accuracy. From the comparison presented, it appears that Galerkin technique offers no substantial advantage over the other finite-difference methods except that of ease in handling boundary conditions as compared with finite-difference methods.