Folding of rocks must balance the deformation of layers with the conservation of volume in a rock mass. This occurs by several mechanisms.
Flexural slip allows folding by creating layer-parallel slip between the layers of the folded strata, which, altogether, result in deformation. The best analogy is bending a phone book, where volume preservation is accommodated by slip between the pages of the book.
Typically, folding is thought to occur by simple buckling of a planar surface and its confining volume. The volume change is accommodated by layer parallel shortening the volume, which grows in thickness. Folding under this mechanism is typically of the similar fold style, as thinned limbs are shortened horizontally and thickened hinges do so vertically.
If the folding deformation cannot be accommodated by flexural slip or volume-change shortening (buckling), the rocks are generally removed from the path of the stress. This is achieved by pressure dissolution, a form of metamorphic process, in which rocks shorten by dissolving constituents in areas of high strain and redepositing them in areas of lower strain. Folds created in this way include examples in migmatites, and areas with a strong axial planar cleavage.