Stopper rod (22) for the continuous casting of molten metal have a stopper rod body (22-3), and a stopper rod tip (22-1) at a lower end of the stopper rod body. The stopper rod tip defines a frustoconically shaped exterior surface (22-1a) which terminates in a recessed nose (22-1b). The recessed nose has most preferably a curvilinear surface (e.g., a spherical segment), but non-curvilinear surfaces (e.g., prismatic, pyramidal, triangular, and quadrangular surfaces) may alternatively be employed. The frustoconically shaped exterior surface (22-1a) of the stopper rod tip most preferably forms an angle with respect to a horizontal plane which is sufficiently great so as to increase the velocity of the flowing molten metal to reduce the boundary