A turbodrill is disclosed for connection to a drill string and has a rotating shaft for turning a drill bit. The turbodrill has rotor and stator blades operated by drilling mud flowing therethrough to rotate the shaft. The shaft is provided with radial/thrust bearing consisting of a pair of annular plates, each of which has conical surfaces supporting a plurality of friction bearing members of polycrystalline diamond. The radial and thrust loads are carried by the wear-resistant diamond bearing surfaces. The bearing members are preferably cylindrical studs having flat faces with flat disc-shaped diamond bearing members supported thereon around the adjacent surfaces of the supporting plates. The faces of the diamond bearings will wear into smoothly mating conical bearing surfaces with use. There are two or more pairs of diamond radial/thrust bearings to handle longitudinal as well as radial loads. The use of the diamond radial/thrust bearings makes it possible to eliminate the lubricant-flooded construction of prior art turbodrills and allow the bearings to be cooled and lubricated be drilling fluid flowing therethrough. The diamond radial/thrust bearings may be used with lubricant-flooded turbodrills and with other types of downhole motor driven drills such as drills driven by positive displacement motors.