The generalized integral transform technique is extended to handle the incompressible Navier-Stokes equations for two-dimensional steady laminar flow in cylindrical geometries. Hybrid numerical-analytical solutions with controlled accuracy are obtained, as a result of an appropriate choice of the associated eigenfunction expansion basis, extracted from the diffusion operator of the stream function-only formulation for this class of problems. The approach is illustrated with a developing laminar flow in annular channel, and numerical results demonstrate the convergence characteristics of the method.