A model predictive control strategy for flexible multibody structures undergoing large deformations is presented. The dynamics of such structures are highly nonlinear, with local effects introduced by the joint constraints and distributed effects arising from the structure’s increased flexibility, from which arbitrary large deflections and rotations can be expected. A modal-based nonlinear reduced order model of an intrinsic description (based on velocities and strains) of geometrically-exact beams is used to underpin the internal model. This low-order model, constructed using the linearised eigenfunctions of the constrained structures, is a set of nonlinear ordinary differential equations in time (i.e. no algebraic equations are present) thus facilitating analysis and demonstrating successful control. Numerical examples are presented based on a very flexible hinged two-link manipulator.