In a twin roll continuous casting apparatus comprising a pair of internally cooled rolls rotating in the opposite direction of each other and disposed parallel to each other with their axes held horizontal, a pair of side dams for forming a pool of molten metal having a predetermined height on the circumferential surfaces of the rolls disposed in the direction perpendicular to the roll axes with a space therebetween approximately corresponding to the width of a metal strip to be cast and a pair of longitudinal dams having respective inside walls along the roll axes to form the pool of molten metal together with the side dams and the circumferential surfaces of the rolls, the improvement wherein one of the longitudinal dams is constructed so that it constitutes an intermediate tundish for pouring a substantially horizontal film flow of molten metal near the level of the surface of molten metal in the pool.