The growth of unstable structures was studied experimentally in layered wax models. The rheological properties of the two wax types were determined independently by a series of cylinder compression tests. Both waxes enhibited (1) a non-Newtonian stress vs strain-rate relationship (2) strain softening and (3) temperature-dependent viscosity. The stress-strain-rate relationships approximated a power-law, with stress exponents of 5 for the microcrystalline wax and 1.8 for paraffin wax. Blocks of paraffin with a single embedded layer of microcrystalline wax were deformed in two-dimensional pure shear with the layer oriented either parallel to the compressive strain axis so that it shortened and folded, or perpendicular to that axis so that it would stretch and boundinage would form. The growth rates of tiny initial disturbances were measured. The growth rates for folding and boudinage were much higher than could be accounted for by theories assuming Newtonian material properties. Theories taking non-Newtonian behaviour into account (Smith, R. B. 1975. Bull. geol. Soc. Am. 86, 1601–1609; Fletcher, R. C. 1974. Am. J. Sci. 274, 1029–1043) better describe the folding growth rates. Boudinage, however, grew almost three times faster than would be predicted even by existing non-Newtonian theory. A possible reason for this discrepancy is that the waxes do not exhibit steady-state creep as assumed in the theory. We, therefore, extend the theory to include strain-softening. The crucial step in this theory is the use of a scalar measure of the deformation as a state variable in the constitutive law. In this way the isotropic manifestation of strain-softening can be taken into account. The analysis shows that strain-softening can lead to greatly increased boudinage growth rates while having little influence on the growth rates of folds, which is in agreement with the experiments.