A bifurcation problem relevant to the process of roll-bonding is studied. The simultaneous rolling of several unbonded layers is modeled as a plane strain compression of the unbonded layers. To gain insight into the phenomenon of tiger banding, the strains at which there can exist bifurcation modes which involve an undulating interface between the layers are computed. Particular attention is focused upon the effect of permitting slip between the layers, in contrast to the assumption of velocity continuity that underlies previous analyses of bifurcation in layered solids. Velocity discontinuity implies that the bifurcation condition depends on the hydrostatic pressure; the consequences of this dependence are highlighted.