Elementary dislocation arrays are applied to multilayered thin films to predict the critical stress required to propagate dislocation loops within individual layers and to study the tendency for deformation to be uniform or localized. The analyses suggest that shearing normal to layers is a mechanically unstable, softening process while stretching parallel to layers produces substantial hardening. Further, films with smaller layer thickness, h, require larger plastic strains to initiate pile-up modes of slip. Although the initial stress required to propagate an isolated loop within a single layer scales as ln(h)/h, there is a minimum h below which the critical stress is predicted to depend only on the resistance of the interface to dislocation transmission.