The invention relates to a roller bearing and seeks to reduce or mitigate the high edge stresses experienced by the bearing elements due to shaft misalignment or distortion under load. The invention provides a roller bearing assembly comprising an outer ring supported in a tubular housing formation associated with a wall of housing, the tubular housing formation extending for at least the axial length of the outer ring wherein the tubular housing formation provides a resistance to radial movement of the outer ring which is greater at one axial end of the outer ring than the other axial end. The low ring of resistance to radial movement may be by selectively profiling the tubular housing formation or rendering it circumferentially discontinuous.