While preparing a digital computer program to examine the behavior of largetaper hub flanges, it was found necessary to use approximations to the Kelvin functions ber x, bei x, ker x, and kei x, and to their first derivatives. To obtain full machine accuracy, the approximations were required to be correct to nine significant figures. Several tabulations of these functions exist, but the only ones considered to be sufficiently accurate were those of Lowell [1] and Nosova [2]; however, limitations of internal memory in the computer used precluded the possibility of storing such tables and interpolating. The functions actually required were Z(x) and Zi' (x) (I < i _ 4), where