A bolt or nut tightening device having an outer shaft and an inner shaft rotatable in directions opposite to each other, the outer shaft having a reaction receiver projecting therefrom sideways and provided with a tightening torque measuring unit, the tightening torque measuring unit comprising a strain sensor, a circuit board, an indicator, a battery, a case for accommodating the circuit board, the indicator and the battery, and a mount tubular member fitted around and rotatable with the outer shaft, the case being attached to an outer peripheral portion of the mount tubular member and projecting toward the same direction as the reaction receiver, the case being so sized as to be hidden by a contour of the reaction receiver and being so positioned as to be hidden behind the reaction receiver when seen from the forward end side of the engaging portion.