We present results of a large-scale atomistic study of the annihilation of oppositely signed screw dislocations in an fcc metal using molecular dynamics (MD) and an Embedded-Atom-Method (EAM) potential for Cu. The mechanisms of the annihilation process are studied in detail. From the simulation results, we determined the interaction energy between the dislocations as a function of separation. These results are compared with predictions from linear elasticity to examine the onset of non-linear-elastic interactions. The applicability of heuristic models for annihilation of dislocations in large-scale dislocation dynamics simulations is discussed in the light of these results.