As the first report, this paper deals with a calculation method of the numbers of stress cycles at the raceway surfaces of the outer sleeve and the shaft, and the equation of the roll body loads. Some points are discussed concerning the calculated results for various shaft strokes. The principal results are as follows : (1) Applying to the new calculation method, which splits both raceway surfaces into small portions, the numbers of stress cycles of those raceways are counted accurately.(2) The roll body loads are considerably small in the case of short shaft stroke, but when the ratio between the shaft stroke and the raceway length of outer sleeve (ls/l) becomes greater than 1, the roll body load of outer sleeve (Qco) has a constant value while the one of shaft (Qcs) has comparatively high increasing ratio.(3) In the case of linear motion ball bearing, probability of flaking due to rolling contact fatigue on the shaft becomes higher than that of the outer sleeve, because of Qco/Qcs=1.25-1.17. Meanwhile, in the case of ball spline, Qco/Qcs≅1 for ls/l≤1 and Qco/Qcs=0.92 for ls/l=10, then the probability of flaking on the outer sleeve becomes higher than that of the shaft. And, if the conformity between ball and raceway groove is reduced, the roll body loads decrease extremely. Further, in the case of ball guide way, the roll body loads are nearly equal to those of the linear motion ball bearing.