Abstract: A support for an ice-beaker comprising a cup-shaped body with a side wall and a base for collecting the water resulting from the progressive melting of an ice beaker housed in the cup-shaped body. The side wall comprises regions, arranged spaced apart on the side wall, for support and restraining the outer wall of an ice beaker. The ice beaker can be produced by an ice-making machine comprising a condensation plate with housings for receiving atomized to form frozen elements. Each housing of the condensation plate comprises a conical side wall and a base wall, the taper of the side being sufficiently wide to bring about the formation of a frozen element which has a central cavity so as to be generally beaker-shaped. In the production method, an intermediate waiting step of predetermined duration is interposed between the interruption of the cooling and the start of the heating of the condensation plate.