Abstract Contact/impact in flexible multibody systems that undergo pre-contact free motion, contact/impact and post-impact constraint motion is modelled. The shortcomings of using coefficients of restitution, penalty parameters and Lagrange multipliers are overcome by using a methodology for modelling non-holonomic hybrid parameter multiple body systems (HPMBS). The minimum set of equations required for the systems were developed using the methodology. All the dynamics of the manipulator (elaborated in the section below) are modelled with very few degrees of freedom. The model was experimentally validated via a planar two-link flexible manipulator that undergoes the complete motion regime. The comparisons show that the model predicts the complete dynamics of the manipulator accurately and the transition between the different modes of motion is seamless.