A linear rolling bearing has an outer housing with a central bore. A plurality of radially inwardly directed axially extending projections in the bore form races for rolling elements under load, and surfaces between the projections serve as return races. A cage within the bore has a plurality of axially extending guide channels, and semicircular guide channels interconnect pairs of the guide channels to form endless channels for the rolling elements. The outer housing has inclined surfaces joining the corresponding races for loaded and unloaded rolling elements, whereby the inclined surfaces steplessly interconnect the respective races and extend radially outwardly from each of these races.