A detailed numerical analysis has been made with respect to the cross slip behavior of a pair of passing screw‐type superlattice dislocations on parallel slip planes in a simple B2‐type superlattice. It is found that below some critical interplanar spacing, cross slip will always occur with mutual annihilation of the two dislocations. This critical spacing in turn establishes the maximum stress required to pass both dislocations past one another (i.e., the maximum strengthening). It is found that the maximum passing stress increases linearly with increasing antiphase boundary energy.