  We show existence of solutions for the equations of static atomistic
nonlinear elasticity theory on a bounded domain with prescribed boundary
values. We also show their convergence to the solutions of continuum nonlinear
elasticity theory, with energy density given by the Cauchy-Born rule, as the
interatomic distances tend to zero. These results hold for small data close to
a stable lattice for general finite range interaction potentials. We also
discuss the notion of stability in detail.
