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The distributions of the hydraulic head and velocity components of the transient groundwater flow in an unconfined compressible aquifer of finite thickness under constant uniform circular recharge are obtained from the linearized mathematical model by the use of integral transforms. The result generalizes Dagan’s (1967) solution which was derived by neglecting the compressibility. By treating the compressibility parameter as a small value, the formula for the hydraulic head is analyzed by asymptotic methods, resulting in approximations to the exact solutions for the head and velocities on small and large time scales. The hydraulic head and flow velocities can be accurately approximated by Dagan's formula for large times; for small times, neglecting the compressibility gives a large relative error but small absolute error.