The dislocation structure of fatigue-hardened pure metals is characterized by large amounts of edge dislocation dipoles which are clustered into multipoles. The most simple model for such dislocation multipoles is a regular arrangement of straight edge dislocations as in a Taylor lattice. Until now, however, only infinitely extended Taylor lattices have been considered and it is not known whether finite sections are stable. Therefore, various sections of the Taylor lattice were numerically relaxed until the stress at the position of each dislocation was zero. It was found that only specific sections are stable. For these stable multipole configurations the applied stress was increased in increments and the new equilibrium positions as well as the reversible plastic deformations corresponding to these rearrangements were determined at each stress increment. Finally the maximum applied stress before disintegration of the configuration was determined and is given as a function of the type and the size of the multipole (up to 361 dislocations). If this maximum applied stress is exceeded, the multipole disintegrates into dipole walls of the type which is experimentally found within persistent slip bands. In the light of these results, various features of fatigue hardening and of fatigue dislocation configurations are discussed.