A cap for a container is made of a material at least part of which is derived from natural fibres. The cap comprises a cup-shaped body having a skirt which extends around an axis and a transversal wall arranged transversally to the axis. A cavity is defined inside the cup-shaped body. The cup-shaped body is delimited by an inner surface facing the cavity and by an outer surface facing the opposite way to the cavity. At least one projecting element projects from a surface of the cup-shaped body selected from either the inner surface or the outer surface. At least one recess is provided at the projecting element on another surface of the cup-shaped body selected from either the outer surface or the inner surface.