  An analytic model of the shear modulus applicable at temperatures up to melt
and at all densities is presented. It is based in part on a relation between
the melting temperature and the shear modulus at melt. Experimental data on
argon are shown to agree with this relation to within 1%. The model of the
shear modulus involves seven parameters, all of which can be determined from
zero-pressure experimental data. We obtain the values of these parameters for
11 elemental solids. Both the experimental data on the room-temperature shear
modulus of argon to compressions of \sim 2.5, and theoretical calculations of
the zero-temperature shear modulus of aluminum to compressions of \sim 3.5 are
in good agreement with the model. Electronic structure calculations of the
shear moduli of copper and gold to compressions of 2, performed by us, agree
with the model to within uncertainties.
