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Three-dimensionsal solutions for the hydraulic head and velocity components for transient groundwater flow in an unconfined compressible aquifer of finite thickness with a rectangular areal recharge source are analyzed using a linearized mathematical model. The solution generalizes Dagan's (1967) results, which were obtained for an idealized aquifer of infinite thickness, and Hantush's (1967) results, which were derived using the Dupuit assumptions. Hydraulic head and velocity components are estimated by asymptotic methods for large times, which are most appropriate for contaminant transport problems. Numerical analysis of the solution demonstrates spatial features of the velocity components in general and a transient effect of upward flow in particular, similar to that found for circular sources (Zlotnik and Ledder, 1992). Obtained formulas show that applicability of the Dupuit assumption for computation of velocity components in an unconfined aquifer is limited to a far-field zone given approximately by |x| > 1.5X, |y| > 1.5Y, where X and Y are the half width and half-length, respectively, of the contaminant source.