Abstract: A cladding for the exterior walls or the roof of a building comprises a plurality of overlapping, profiled and elongate panels of e.g. sheet metal or plastic attached to supporting rails extending in spaced relationship over the surface to be covered in a direction intersecting the longitudinal directions of the panels. Each supporting rail has a series of rigid fastener means each with a dovetail-shaped incut. One longitudinal marginal portion of each panel has a resiliently deformable cross section adapted for snapping into the incut of one fastener means on each of at least two adjacent supporting rails and forms a groove with undercut side walls opening towards the front or outer side of the cladding. The opposite longitudinal marginal portion of each panel also has a resiliently deformable cross section adapted to partly enter said groove of an adjacent panel and to be retained therein in a clamped position in which at least one of the two interengaging marginal panel portions is slightly deformed.