Pileups of screw dislocations against an inclined bimetallic interface are considered. It is assumed that differently oriented pileups are either under the same remote uniform loading, or under the same resolved shear stress along the pileup direction for any orientation of the interface. The distributions of dislocations and the lengths of pileups are substantially different for differently oriented interfaces, particularly in the case of the same remote loading. The interface stresses are also strongly depended on the pileup orientation. The maximum stress can be higher for a pileup along an inclined direction than along the direction orthogonal to the interface. The back stress behind a pileup is evaluated and discussed.