An improved description of copper- and iron-cylinder impact (Taylor) test results has been obtained through the use of dislocation-mechanics-based constitutive relations in the Lagrangian material dynamics computer program EPIC-2. The effects of strain hardening, strain-rate hardening, and thermal softening based on thermal activation analysis have been incorporated into a reasonably accurate constitutive relation for copper. The relation has a relatively simple expression and should be applicable to a wide range of fcc materials. The effect of grain size is included. A relation for iron is also presented. It also has a simple expression and is applicable to other bcc materials but is presently incomplete, since the important effect of deformation twinning in bcc materials is not included. A possible method of acounting for twinning is discussed and will be reported on more fully in future work. A main point made here is that each material structure type (fcc, bcc, hcp) will have its own constitutive behavior, dependent on the dislocation characteristics for that particular structure.