A process for permanently modifying the shape of hair by wrapping hair in multilayered, deformable sheets of material comprising a first layer of a perforated, deformable, and semi-rigid material, and a second layer of material containing a thiol reducing composition in an amount effective for permanently modifying the shape of hair, wherein the first layer is placed on or attached to the second layer; providing a desired shape to the multilayered, deformable sheet of material which is wrapped around the hair; and applying an oxidizing composition comprising an oxidizing agent capable of reconstituting the disulfide bonds of the hair, wherein the oxidizing composition is applied either before or after liberating the hair from the multilayered, deformable sheet of material. In another variation, the hair is pre-treated with the reducing composition and then wrapped in a single deformable sheet for shaping. Multicomponent kits for use in the processes of the invention.