A method and an apparatus for bending pipes by clamping one end of the pipe between a formed roll and a rotary base and by turning the rotary base so that the pipe may be bent along the outer periphery of the formed roll. A mandrel supported by a mandrel bar is arranged inside the pipe at a position corresponding to a position slightly behind where the pipe is clamped between the formed roll and the rotary base. The rear end of the mandrel bar is held in place by a pressurizing device so that the mandrel can be held fixed at said predetermined position inside the pipe. At the same time, a vibrating device attached to the mandrel bar causes the mandrel to continuously reciprocate in the axial direction of said mandrel bar, whereby flattening of the pipe which occurs when the pipe is bent along the outer periphery of the formed roll can be corrected by the reciprocation of the mandrel. As a result, the radius of curvature R of the pipe can be made smaller than R=3D, where D is the diameter of the pipe.