The annihilation of dislocations by cross-slip is studied by numerical simulation of infinitely long dissociated screw dislocations, allowed to move in an elastically anisotropie crystal. The external load is along [123] and cross-slip is permitted both on the octahedral and on the cube plane. The latter, together with cube slip, is thermally activated. Anisotropie elasticity modifies the properties of cross-slip significantly. Under the conditions of the simulations, the processes of APB jumps (APBJs) and repeated APB jumps (RAPBJs) can be largely promoted by interactions with other dislocations, while it is much less likely to occur at an isolated dislocation submitted to the same applied stress. The encounter of dislocations of opposite signs produces dipoles which may or may not tend to annihilate by cross-slip. APB tubes may form upon annihilation under certain circumstances again largely controlled by elastic anisotropy.