Pillow or mattress having a comfort layer (5) which is made of natural or synthetic latex, polyurethane foam or another elastic material. The comfort layer 5 is provided with interrupted incisions (6) through the layer 5, along mainly parallel lines 7, and the layer (5) forms at least a part of a jacket around a core (2) of the pillow or mattress that is stretched in a lateral direction (P) which is mainly transverse to the direction of the above-mentioned lines (7) in order to open the incisions (6) so as to form passages (8) through the comfort layer (5).