  We analyse the equilibrium pile-up configurations of infinite periodic walls
of edge dislocations which are forced against an impenetrable obstacle by a
constant applied shear stress. Numerically generated density distributions
exhibit two distinct regions, for each of which we provide an interpretation
and an analytical prediction. Near the obstacle, the influence of neighbouring
slip planes may be neglected and the classical solution for a single slip plane
applies. At a larger distance a linear decay is obtained. The characteristic
length scales of the two parts of the pile-up are shown to depend differently
on the parameters of the problem.
