A near optimal minimum-maximum rational approximation to the Bickley functions Kis(x) for s = 1, 2, 3 and 0 x < 7, and Kis(x) for s = 13, 14, 15 for 7 x < 600 with a relative error of <10-12. The above initial approximations combined with a recurrence relation yield a stable method of computing Kis(x) for the prescribed accuracy except for the region S: {(x, s): x 28, s > 15}.