A panel-like/sheet-like finishing element (11) for covering floors and walls, for example in the renovation of old buildings, is provided with heat-insulating and sound-absorbing properties if its interior (15) is provided, between outer covering layers (12, 13), with channel-forming undulating supporting structures (16) filled with high-density coarse granules (21). The supporting structures (16) are connected to the covering layers (12, 13) along the vertex lines (17) so as to provide wet-strength action, and the interior (15), between these covering layers, is sealed by enclosing edging strips (19) to provide wet-strength action, with the simultaneous inclusion of moisture-tight, but vapour-permeable, supporting layers (20) on covering layers (12, 13). If this finishing element (11) is mounted vertically, the granule-filled channels (14) run horizontally.