In this paper, the free oscillations of a masonry panel made of unilateral No-Tension material are analysed, by adopting essentially the model proposed by Jacques Heyman. The aim of this analysis is to quantify the role of the elasticity in compression in the geometrically nonlinear dynamical response of Masonry-Like structures. Therefore, two unilateral models are considered: the first model assumes that the material is rigid in compression, the second one that the material is elastic in compression. Different levels of stiffness, in a range that covers realistic values of the Young modulus, are explored and the response of a simple panel subject to a fixed vertical compression and to different initial lateral disturbances are compared in order to estimate the effect of elasticity. As time histories for rigid and elastic panels display, the response of the rigid block is periodic and the response of the elastic block is quasi-periodic. In both cases the oscillation periods are visibly dependent on the amplitude. The periodicity of the elastic panels and its dependence on the amplitude is detectable also in the purely elastic phase, and is due to the physical nonlinearity induced by the unilateral material restrictions. The comparison between rigid and elastic time histories shows the main differences between the rigid and the elastic cases and allows to quantify the accuracy of the rocking-like assumption compared with the “harmonic type” simplification.