Summary: The approach developed in preceding papers is extended to derive the equilibrium positions of \(n\) edge dislocations in a linear pile-up stressed by a constant applied loading against an interface in a bimetallic solid. As \(n\rightarrow \infty \), the dislocations in the inner region are located with sufficient accuracy that the stress distribution at the interface can be evaluated by a simple computational procedure. Such a prediction is impossible using a conventional continuum dislocation theory.