A method and apparatus for manufacturing a composite material part from a preform of fibers pre-impregnated with resin. The method includes laying the preform on a laying surface of a tool with a peripheral shoulder, covering the preform with a conforming plate delimited by a peripheral edge which extends beyond the peripheral flank of the preform over the entire periphery of the preform, using shims calibrated to position the conforming plate, the shims being arranged between the support surface of the peripheral shoulder and the peripheral edge of the conforming plate, removing the calibrated shims, arranging a seal connecting the conforming plate and the tool all around the preform, and polymerizing the preform.