The available approaches for analyzing pulse tests assume that the initiating pressure pulse is instantaneous. However, in practice this is difficult to achieve due to equipment response lags. A new model is derived which includes pulses of finite duration. This model is an extension of the instantaneous model of Bredehoeft and Papadopulos (1980), who presented an integral expression to explain behavior during a pulse test. In this paper, equations are derived for both instantaneous and finite duration cases in Laplace space. These equations are numerically inverted to real space using the algorithm of Stehfest (1970). The finite duration pulse test model differs from the instantaneous model in an integral term which acts as a correction to the flow response. In order to numerically invert the finite duration equation the integral term is first numerically evaluated. An approximation is introduced to enable the explicit numerical integration of this term. The use of the instantaneous pulse model to analyze pulse tests which involve a finite duration results in error in the estimation of formation hydraulic properties. In one example considered, where the pulse was 30 s, the error was near zero for a specific storage capacity less than 1¿10-9 m-1, and the formation conductivity less than 1¿10-9 m s-1. However, for the same test conditions, a conductivity of 1¿10-8 m s-1 and a specific storage capacity of similar magnitude would result in an error of approximately 50% in conductivity. ¿ American Geophysical Union 1994