A seal packing assembly apparatus which assembles a seal packing into a core plate used as a component of a heat exchanger, which apparatus is provided with rollers which push a seal packing into a groove of a core plate while moving by rolling along the groove and guide members which abut against the core plate, the rollers being supported so as to displace along the shape of the core plate by the reaction force which the guide members receive from the core plate, whereby the reliably of assembly of the seal packing is improved.