An analysis is presented which predicts the properties of an arbitrarily thick turbulent boundary layer for incompressible axial flow past a long cylinder. The approach makes use of a modified form of the law-of-the-wall, deduced by G. N. V. Rao, which properly accounts for transverse curvature effects. Using this law, the theory which follows is equivalent to an exact solution to the axisymmetric equations of continuity and momentum for zero pressure gradient. Numerical results show that curvature increases skin friction and overall drag and decreases the boundary layer thickness and the integral thicknesses. The velocity profile is flattened and the shape factor approaches unity at large curvature. Comparison with several sources of friction data show better overall agreement than previous theories, except for an unexplained discrepancy with data for moving nylon fibers at very small radius Reynolds numbers.