The present invention relates to teats that are specially designed for breast-fed babies, of any species, with a cleft palate. The tip of these teats is longer than that of a standard teat and the palate side forms a dihedral angle, the vertex of which is truncated in order to form a raised band that attaches to the breast-fed baby's palate cleft, thereby preventing milk from passing to the airway, thus preventing aspiration pneumonia and other, associated infections. The invention likewise relates to the method for producing these teats by obtaining a mould of the cleft palate and using heat-mouldable plastic sheets and a thermo-vacuum machine. The personalized teats can be used when feeding babies and the young of not only companion animals of particular economic value, but also experimental animals, allowing the creation of an animal-experimentation model for the study of this extremely complex pathology.