A Laplace transform solution is presented for the problem of flow to a partially penetrating well of finite diameter in a slightly compressible water table aquifer. The solution, which allows for evaluation of both pumped well and observation piezometer data, accounts for effects of well bore storage and skin and allows for the noninstantaneous release of water from the unsaturated zone. For instantaneous release of water from the unsaturated zone the solution approaches the line source solution derived by Neuman as the diameter of the pumped well approaches zero. Delayed piezometer response, which is significant during times of rapidly changing hydraulic head, is included in the theoretical treatment and shown to be an important factor in accurate evaluation of specific storage. By means of a hypothetical field example it is demonstrated that evaluations of specific storage (Ss) using classical line source solutions may yield values of Ss that are overestimated by a factor of 100 or more, depending upon the location of the observation piezometers and whether effects of delayed piezometer response are included in the analysis. Theoretical responses obtained with the proposed model are used to suggest methods for evaluating specific storage.