The response of a fully penetrating well to a slug test in a confined aquifer can be described by a single differential equation that is valid for any degree of damping. Although an analytical solution is not available, numerical methods are readily applied. The impact of nonlinear terms becomes significant only when the initial water level displacement is a large fraction of the effective water column height. Previously published approximate solutions for underdamped response are sometimes very accurate. Copyright 1985 by the American Geophysical Union.