Numerical solutions are given for surface waves generated by underwater explosions. The shallow water approximation is used for the governing equations. An axisymmetric initial impulse is applied to the surface of the water. The initial impulse distribution is taken from the results obtained by Falade and Holt. Due to the unavailability of the initial displacement distribution, the latter is assumed to be zero, but the method can work for the case when both initial impulse and displacement are presented. Glimm’s scheme is used to obtain the solution for the shallow water equations. The scheme was developed to solve one‐dimensional gas dynamic problems. With slight modification, the scheme can be used for the shallow water equations. It is tested successfully on the dam break problems. The calculations confirm the existence of the upper critical depth effect, namely, that for near surface explosions, the maximum amplitude surface wave is that generated by an explosion just below the surface.