This paper reports the results of a study of some two- and three-dimensional cases of stress distribution with particular reference to shafts having fillets or transverse holes, these being of considerable practical importance. To determine the stress-concentration factor kt in such cases, strain measurements were made, using a specially developed extensometer with a gage length of 0.1 in. The results of these strain measurements indicate that for shaft fillets in bending (three-dimensional case) the stress-concentration factor kt is little different from the values obtained photoelastically on flat specimens having the same r/d ratio (a two-dimensional case). A comparison of these values of kt (both for shafts with fillets and with transverse holes), with data from fatigue tests, leads to the following observations: (1) In some cases fatigue results are quite close to theoretical stress-concentration values. (2) Fatigue results for alloy steels and quenched carbon steels are usually closer to theoretical values than are the corresponding fatigue results for carbon steels not quenched. (3) With decrease in size of specimen, the reduction in fatigue strength due to a fillet or hole becomes somewhat less; and for very small fillets or holes the reduction in fatigue strength is comparatively small. (4) Sensitivity factors determined for small specimens should not be applied to the design of machine parts regardless of size.