The Ritz method was used in this paper for the flexural analysis of a statically indeterminate Euler – Bernoulli beam with a prismatic cross section. The beam considered was a propped cantilever of length, l, fixed at x = 0, and simply supported at x = l; and carrying a linearly distributed transverse load on the longitudinal axis. Two cases of coordinate (basis) functions were studied. In the first case, the basis functions were constructed to satisfy the deflection boundary conditions, but not the force boundary conditions. In the second case, the basis functions were constructed to satisfy all the boundary conditions. It was found that the stiffness equations formed with the basis functions that satisfied all the boundary conditions gave the exact solutions for deflection, bending moments and shear force distributions along the beam’s longitudinal axis. The effectiveness of the Ritz method for solving statically indeterminate Euler Bernoulli beam flexure problems was thus highlighted.