Abstract: An inertia force balancing apparatus for a machine haivng a reciprocating heavy object, such as a Pilger rolling mill provided with a heavy object stand having a pair of Pilger mill rolls and horizontally supported such as to be reciprocable and with a drive device for imparting reciprocating motion to the Pilger mill stand by a motive power converted from rotational motion, into reciprocating motion. A spring device secured at its end to the heavy object and adapted to balance the inertial force of the reciprocating motion of the heavy object. A control device is provided for changing the spring force of the spring device in accordance with the rotational speed of the rotational motion of the drive device.