Nonlinear normal modes (NNM) are useful tools to study nonlinear vibrations for mechanical systems. We are interested in finding NNM in the context of perfectly elastic unilateral contact. To this end is investigated a discrete model representing a flexible thin rod in contact against a frictionless rigid foundation. This one dimensional model is essentially given by coupled harmonic oscillators with an unilateral rigid contact against a wall. We assume that the contact preserves energy. A natural mathematical formulation is derived and important features for this N dof system are explored: grazing contact, periodic solutions.