The development of multiple solutions for orthotropic cantilever beams in a fully three-dimensional setting is investigated. The governing equations are solved using an iterative shooting procedure that converts the original boundary value problem into a sequence of initial value problems that converge to the desired solution. This method is well suited to finding multiple equilibrium solutions. Several classes of equilibrium configurations are described and illustrated including planar shapes, buckled planar shapes and fully three-dimensional configurations which appear far removed from the initial plane of loading. The solutions for the planar shapes and the buckled configurations compare favourably to previously published results. The development of the far-removed shapes is shown to be qualitatively similar to that of the planar shapes. The behaviour is shown to be highly dependant upon the aspect ratio of the cross-section. For certain aspect ratios it is shown, somewhat surprisingly, that out-of-plane equilibrium solutions can exist at loads below those required for multiple planar solutions.