Unlike radial flow to a well the pattern of flow to a trench changes with time. Flow vectors at early times are normal to the surface of the trench and affect a small area, whereas after a long period of pumping they converge radially from large distances. This changing flow pattern controls performance, and ignoring the transient effects can result in errors when predicting flows in the vicinity of a trench. The method of instantaneous source functions is used to obtain transient analytical solutions to a variety of two- or three-dimensional problems related to interceptor trenches. Drawdown in the vicinity of a trench that is pumped at constant rate and discharge from a trench that is held at constant drawdown are given as functions of time. Travel times to trenches in regional flow fields are also obtained and expressed in dimensionless form. Applications of the results include improved predictions of the performance of environmental applications of interceptor trenches and estimation of aquifer parameters from the analysis of pump tests from trenches. ¿ American Geophysical Union 1994