Abstract: A test function by using the Bessel function and basic function,which satisfies constant-head and no flow boundary conditions,is put forward to describe unsteady groundwater flow in the cylindrical coordinate system.Based on Galerkin’s method,semi-analytical finite layer equations are derived in the non-homogeneous and anisotropic layered leaky confined aquifers.The finite layer method(FLM) for the unsteady groundwater flow is presented in the cylindrical coordinate system.A computer program is developed for solving the finite layer equations.Numerical examples are presented and compared with the analytical solutions to demonstrate the validity and efficiency of the present method.