A new method is demonstrated for finding the bending moments and deflections of a twisted cantilever beam due to both transverse and axial loads. The actual physical system is approximated by a lumped or discrete system which is handled by matrix methods. It is shown that good accuracy may be expected even with slide-rule computation, since the method corresponds to a set of successive numerical integrations. The setup is particularly adapted to investigating the effects of changing the initial offset and of different rotating speeds of a propeller or turbine blade. In addition, a procedure is demonstrated for the application of a successive approximation method, analogous to a Stodola solution, to a problem which would otherwise show oscillating divergent results.