A quantitative theory of dislocation multiplication in the early stages of glide band formation is proposed. It is based on the model of double cross slip suggested by W. G. Johnston and J. J. Gilman [J. Appl. Phys,31, 632 (1960)]. Moving screw dislocations are believed to undergo cross slip but return in a random fashion into slip planes parallel to the original slip planes. The edge dislocation parts created between the two cross slip events cannot follow the screw dislocations, thus creating dipole dislocation trails. If the distance between the dipole dislocations is large enough that they pass each other under the applied stress, a new dislocation loop is formed in the parallel plane and the original dislocation is restored completely in its glide plane. On this basis, expressions for the number of trails and for the number of new loops created directly and indirectly by a moving dislocation are derived. The results of the theory are found to be in good agreement with the limited available data, namely the measurements on dislocation multiplication in LiF by W. G. Johnston and J. J. Gilman [J. Appl. Phys.30, 129 (1959)].