A turbine bucket adapted to be supported on a turbine or rotor wheel includes an airfoil portion extending radially relative to a longitudinal axis of the rotor wheel and having a leading edge, a trailing edge, a pressure side and a suction side. At least one tip shroud extends in opposite circumferential directions, the shroud having a first hard face adapted to engage a mating second hard face on a shroud extending circumferentially from an adjacent bucket. The first hard face defined by a surface portion that varies circumferentially with an increasing radius as measured from the longitudinal axis of the rotor wheel.