  The shear viscosity $\eta$ in the van der Waals excluded volume
hadron-resonance gas model is considered. For the shear viscosity the result of
the non-relativistic gas of hard-core particles is extended to the mixture of
particles with different masses, but equal values of hard-core radius r. The
relativistic corrections to hadron average momenta in thermal equilibrium are
also taken into account. The ratio of the viscosity $\eta$ to the entropy
density s is studied. It monotonously decreases along the chemical freeze-out
line in nucleus-nucleus collisions with increasing collision energy. As a
function of hard-core radius r, a broad minimum of the ratio $\eta/s\approx
0.3$ near $r \approx 0.5$ fm is found at high collision energies. For the
charge-neutral system at $T=T_c=180$ MeV, a minimum of the ratio $\eta/s\cong
0.24$ is reached for $r\cong 0.53$ fm. To justify a hydrodynamic approach to
nucleus-nucleus collisions within the hadron phase the restriction from below,
$r~ \ge ~0.2$ fm, on the hard-core hadron radius should be fulfilled in the
excluded volume hadron-resonance gas.
