We describe a version of the smooth particle hydrodynamics (SPH) metho
d suitable for modeling solids. The model includes strength and implem
ents a von Mises yielding relation for stresses beyond the Hugoniot el
astic limit. At lower stresses associated with brittle failure we use
a rate-dependent strength based on the nucleation and growth of explic
it Weibull flaws. We illustrate the capabilities of our fracture model
by examining the propagation of cracks in a simple tensile rod, and b
y comparing simulations with laboratory experiments for high speed imp
acts and cratering.