A header and tube assembly for use in a shell-and-tube type heat exchanger formed of a header plate having a plurality of spaced apart openings therethrough, each opening having a large cross-sectional area in the portion adjacent the header outer surface than the cross-sectional area adjacent the inner surface, a tube received in each of the openings, each tube having an outer end extending at least even with the header outer surface, and a sealer filling each of the openings in the header and surrounding the tube in the openings to thereby secure each tube in a leak-proof arrangement. In one embodiment, each opening in the header is of conical cross-sectional configuration, and in another embodiment, each opening in the header has a smaller cross-sectional portion adjacent the header inner surface dimensioned to snugly receive the tube and a larger cross-sectional portion adjacent the header outer surface to receive the sealer therein.