Folds in rock provide opportunities for establishing how fabric and deformation mechanisms vary with local variations in strain and strain rate, and strain distribution in folds should, in principle, provide information on rheological conditions during folding. To investigate this, we use finite element models to simulate buckling in single-layer folds in incompressible, power-law materials in plane strain. Numerical results show that the pattern of strain variation in buckle folds is sensitive to variations in the power-law exponent, nL, of the stiff layer. For a given amplitude, wavelength/thickness, and ratio of viscosities, m, of layer to matrix, strain and strain gradient along the axial trace increase more rapidly away from the neutral surface (on both sides) for power-law (nL > 1) materials than for Newtonian (nL = 1) materials. Buckling strain is superimposed on early uniform layer-parallel shortening, which becomes greater as initial amplitude decreases and as nL and m decrease. The effect of this superposition can best be described by reference to the infinitesimal neural surface (INS) and finite neutral surface (FNS), which vary in position with degree of overall shortening. The INS and FNS move from the outer arc towards the inner arc during buckling, the latter following the former. Thus, at any stage of folding, the layer can be divided into three zones with different coaxial, non-linear strain histories. Fabric in natural folds is expected to reflect such unsteady flow conditions.