Buckle-fold development in single layers has been simulated by means of a two-dimensional finite element model incorporating incompressible power-law viscous fluids. We have produced folds with the stiff layer initially parallel to and oblique to the bulk maximum shortening direction and investigated how fold growth rates and geometry vary as functions of viscosity ratio and power-law exponent. Results for single-layer buckling and the related instabilities of boudinage, mullions and inverse folding closely match theoretical predictions in terms of initial growth rates, which depend strongly on the power-law exponent. The results further show that the fold shape is sensitive to changes in the power-law exponent of the stiff layer. The most striking feature is that the fold hinges become sharper and the limbs become relatively longer and straighter as the exponent increases. Asymmetry of folding can arise in bulk pure shear. Models of asymmetric folds with inclinations of the stiff layer of up to 30° have been made. The results indicate that initial growth rates are independent of the inclination of the stiff layer. Results of this work suggest that a number of geometrical properties of folds may be useful in providing information on the rheological behavior of rocks deformed under very slow natural conditions.