The aim of this paper is to study the effect of relaxing the assumption in the Peierls analysis that the dislocation must be wide compared to the atom spacing. To do this the use of the continuum description of the in-plane strains caused by the presence of an edge dislocation is replaced by an atomistic interaction taken to be linear elastic. It is found that in this case the inplane interactions give a contribution to the overall misfit energy changes that are not present in the Peierls analysis because of the use of a continuum approach. This contribution modifies these energy changes so that the total misfit energy is a minimum at the conventional low energy positions (whereas in the Peierls analysis it is a maximum) and gives values of the Peierls stress in reasonable agreement with those measured.