A method of production of an α+β-type titanium alloy part for a motorcycle, car, or bicycle which has a high Young's modulus (rigidity) in the axial direction of the shaped product and a bolt, engine valve, or connecting rod made of an α+β-type titanium alloy and a method of production of the same, wherein an α+β-type titanium alloy is heated at the temperatures giving the β-single phase, then is uni-directionally hot rolled, the plate is machined so that a direction vertical to both the hot rolling direction and thickness direction (width direction) corresponds to the direction in which high rigidity is demanded in the finished part, that is, the axial direction of the bolt, engine valve, or connecting rod, and the X-ray diffraction intensities I(0002), I(10-10), and I(10-11), of the (0002) plane, (10-10) plane, and (10-11) plane of the titanium α-phase measured at the cross-sections vertical to the longitudinal axial direction of the parts satisfy I(0002)/[I(10-10)+I(10-11)]≦1.