To provide a rolling bearing having better reliability and durability capable of resisting extreme operating conditions under which bearings are used by being immersed in fluids having low viscosity and cryogenic temperature.

The rolling bearing is composed of an inner race, an outer race, and a plurality of rolling elements incorporated in the space between the inner and outer race, and the inner or the outer race is engaged with an axis or a housing so that hoop stress of the engaging part shows 100-500MPa and at the same time, when a pitting index (P.I) is defined as P.I.=1[%Cr]+3.3[%Mo]+30[N%]-45[C%], a martensitic stainless steel of P.I.=-5 to 40 is used.