This research studied the problem of varying depth and varying elastic properties along flexural member lengths subjected to generalised loading, with such members considered to be nonhomogeneous and non-prismatic. The differential equation for classical thin beams was thus derived and the finite differences used in solving this equation. Fortran programs were written to solve the problem in finite differences, and three-dimensional elements were used to simulate or model the beams in finite element ABAQUS software. A parametric study of the influence of beam width, depth, load nature, and boundary conditions on deformations and internal forces was thus accomplished. The maximum variation in deformations seen between this study and previous studies was 8%. The deflection of the non-prismatic beam was reduced by 31% when the ratio of the beam moment of inertia at different sections increased by up to three times, while, the moment capacity and the right end support shear capacity were increased by 78% and 50%, respectively.
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