In this work we propose a new methodology to simulate sticking motions occurring in vibro-impacting continuous systems. We have developed this method in the framework of the coefficient of restitution approach. During the sticking phase, the sticking constraints are imposed exactly using a Lagrange multiplier, which represents the reaction between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The proposed method does not require the mode-shapes during the sticking phase, unlike the mode-switching method. The developed methodology is supported by illustrative numerical simulations. © 2013 ASME.