ESDU 69017 gives a method of calculating the slope and deflection at any point along the length of a shaft or beam of constant or stepped cross section under any number of point loads, distributed loads and applied moments. A calculation procedure is first described for cases in which the shaft is simply-supported and carries point loads and moments in one plane. Details are given of a means of extending the calculation procedure to include treatment of uniformly distributed loads, overhung loads, shafts supported on three bearings and out-of-plane loads. The procedure is based on an approximation to the Engineers Bending Theory whereby the inertia of the shaft is fitted by a Fourier series. The degree of approximation for each type of shaft covered is shown. The normal limitations of Engineers Bending Theory apply, so that no allowance is made for deformations due to shear. ESDU 69017 may be applied to shafts with shrunk-on collars of the same modulus of elasticity.