Abstract: A method for curvilinearly converting of web or sheet material by compression of the material between an upper table and a lower table. The tables are each connected to a respective supporting structure and operate conjointly on either side of the plane of travel of the material along a longitudinal axis. During the compression phase, there is a phase of essentially unidirectional intentional elastic deformation of a structure of one of the tables. The deformation increases and then decreases as the curvilinear surface of one table rolls past the other table, for providing generally more uniform compression as the surface rolls. An apparatus for the compression includes the structure described.