The upper surface of the ski has hollows which hold reinforcement (20). These are a pile of rigid flat layers (21, 22, 26) and the top layer (21) is fixed to the inner surface of the ski. Two films (23, 24) of an elastomer material are put between the layers at the zones of maximum deformation. The ski is made in a mould and the components of an expansible foam are injected into the space between the sole and the upper surface. The heat produced as the foam expands fixes the layers to the upper surface of the ski.