The authors study a biologically relevant version of a mechanical model for morphogenesis proposed by Oster, Murray and Harris [J. Embryol. Exp. Morph. 78, 83-125 (1983)]. A nonlinear bifurcation analysis of the partial differential system is presented. In the one- dimensional version, the derivation of the amplitude equation involves a nonstandard element. The analysis of a caricature of the two-dimensional system predicts the formations of rolls and hexagons. The biological significance of the results to feather germ formation is briefly discussed.