Kink-bands and associated kink folds are common structures in layered or foliated rocks. Their presence indicates that the dominant rheology of rocks was of anisotropic plasticity. We apply the commercial finite difference code FLAC and supplemental programs that we developed to address an outstanding problem of kink-band formation, namely what controls the onset and subsequent development of kink-bands. We use Mohr-Coulomb solid with an embedded planar anisotropy to simulate well-layered rocks. When subjected to anisotropy-parallel shortening, two competing deformation mechanisms are observed and their relative significance depends on the ratio (m) of the strength of the Mohr-Coulomb solid to that of the anisotropy. At a given strength of the solid, when m is low, the mode of deformation is strain localization leading to development of conjugate kink-bands. As m increases, strain localization gradually gives way to distributed deformation by kinking - formation of kink folds with axial planes at high angles to the shortening direction. Although as bulk strain increases, kink-band boundaries migrate through material and rotate to higher angles to the shortening direction, this migration and rotation is limited and is not the primary mechanism for kink fold development.