Fault‐related folds develop due to a combination of slip on the associated fault and distributed deformation off the fault. Under conditions that are sufficient for sedimentary layering to act as a stack of mechanical layers with contact slip, buckling can dramatically amplify the folding process. We develop boundary element models of fault‐related folding of viscoelastic layers embedded with a reverse fault to examine the influence of such layering on fold growth. The strength of bedding contacts, the thickness and stiffness of layering, and fault geometry all contribute significantly to the resulting fold form. Frictional contact strength between layers controls the degree of localization of slip within fold limbs; high contact friction in relatively thin bedding tends to localize bedding slip within narrow kink bands on fold limbs, and low contact friction tends to produce widespread bedding slip and concentric fold form. Straight ramp faults tend to produce symmetric folds, whereas listric faults tend to produce asymmetric folds with short forelimbs and longer backlimbs. Fault‐related buckle folds grow exponentially with time under steady loading rates. At early stages of folding, fold growth is largely attributed to slip on the fault, but as the fold increases amplitude, a larger portion of the fold growth is attributed to distributed slip across bedding contacts on the limbs of the fold. An important implication for geologic and earthquake studies is that not all surface deformation associated with blind reverse faults may be attributed to slip on the fault during earthquakes.