  We calculate the coefficient of restitution, $\epsilon$, starting from a
microscopic model of elastic disks. The theory is shown to agree with the
approach of Hertz in the quasistatic limit, but predicts inelastic collisions
for finite relative velocities of two approaching disks. The velocity
dependence of $\epsilon$ is calculated numerically for a wide range of
velocities. The coefficient of restitution furthermore depends on the elastic
constants of the material via Poisson's number. The elastic vibrations absorb
kinetic energy more effectively for materials with low values of the shear
modulus.
