  We study a simple model of a bouncing ball that takes explicitely into
account the elastic deformability of the body and the energy dissipation due to
internal friction. We show that this model is not subject to the problem of
inelastic collapse, that is, it does not allow an infinite number of impacts in
a finite time. We compute asymptotic expressions for the time of flight and for
the impact velocity. We also prove that contacts with zero velocity of the
lower end of the ball are possible, but non-generic. Finally, we compare our
findings with other models and laboratory experiments.
