A mask for supplying gas under pressure to the nasal airway of an infant human includes a manifold for supplying air to an aperture in the mask. A shaped membrane structure formed from a thin walled membrane defines an enclosure for receiving at least the nares of an infant human nose and a generally trapezoidal aperture adapted to fit around the nasal area of the infant human. Part of the membrane around the aperture is sufficiently flexible to mold to the shape of the infant human's nasal area or is contoured to generally match the contours around that nasal area while the membrane structure itself has sufficient rigidity to support the weight of the backing plate without collapsing. The provision of a generally trapezoidal rather than the generally triangular apertures for fitting around the nares provides a substantially improved fit when the mask is used with infants. The molding or contouring of the membrane structure around the aperture to match the shape of the infant's facial contours around the nasal area including the provision of a generally planar portion surrounding the aperture is also important in ensuring a comfortable fit and an effective seal. The mask is entirely formed from a flexible elastomeric material for reason of comfort and function.