The invention relates to a method and an apparatus for jointing members made of plastic-coated paper or board. In accordance with the invention, the sealable members are retained in position with clamps (8) and sealing is performed with a laser sealing means (7) moving along the sealing line, a means (9) for opening the seal point pressing the members apart to continue keeping the seal point open, a laser beam (11) being directed to the open seal point for melting the coating plastic and a means (12) for closing the seal pressing finally the members against each other, the plastic jointing the members when solidified. The method is applicable to lateral sealing of bag or container packages formed of blanks (1), among other things.