Apparatus for moulding containers from a strip (C) of paper material, comprising a stationary die-holder plate and a movable die-holder plate which is movable with respect thereto between a distal, opened position, and a proximal, closed position, in which: - the stationary die-holder plate includes a respective stationary die half and the movable die-holder plate includes a respective mobile die half , wherein, in the closed position, the stationary die half and the mobile die half together define an impression corresponding to a container provided with a bottom , a side wall and a flat perimeter portion cantileverly extending from the side wall , and - a curling member , a permanent pleating/ wrinkling member and a cutting blade are concentrically and successively provided around the mobile die half , and - a counter curling member , a counter permanent pleating / wrinkling member and a counter cutting blade are concentrically and successively arranged around the stationary die half , and wherein - the cutting blade and the counter cutting blade interact to cut, from the starting strip (C), a blank (C') having dimensions proportional to the dimensions of the container to be moulded, the permanent pleating / wrinkling member and the counter permanent pleating / wrinkling member interact to permanent pleat or wrinkle a peripheral crown (C1) of said blank (C') by at least part of both the side wall and the flat perimeter portion of the container (C') being moulded, and the curling member and the counter curling member interact to form a curled edge extending from the flat perimeter portion of the container (C') being moulded, characterized in that the mobile die half can be at least partially inserted into the counter curling member to form the curled edge of the container between the lying plane of the related flat perimeter portion and the bottom of the container itself. - the stationary die-holder plate includes a respective stationary die half and the movable die-holder plate includes a respective mobile die half , wherein, in the closed position, the stationary die half and the mobile die half together define an impression corresponding to a container provided with a bottom , a side wall and a flat perimeter portion cantileverly extending from the side wall , and - a curling member , a permanent pleating/ wrinkling member and a cutting blade are concentrically and successively provided around the mobile die half , and - a counter curling member , a counter permanent pleating / wrinkling member and a counter cutting blade are concentrically and successively arranged around the stationary die half , and wherein - the cutting blade and the counter cutting blade interact to cut, from the starting strip (C), a blank (C') having dimensions proportional to the dimensions of the container to be moulded, the permanent pleating / wrinkling member and the counter permanent pleating / wrinkling member interact to permanent pleat or wrinkle a peripheral crown (C1) of said blank (C') by at least part of both the side wall and the flat perimeter portion of the container (C') being moulded, and the curling member and the counter curling member interact to form a curled edge extending from the flat perimeter portion of the container (C') being moulded, characterized in that the mobile die half can be at least partially inserted into the counter curling member to form the curled edge of the container between the lying plane of the related flat perimeter portion and the bottom of the container itself. <EOS>