A method of making a straw stopper consisting of a substantially cylindrical support through which there is a substantially coaxial orifice and a microporous and hydrophobic membrane welded to one end of said cylinder substantially perpendicularly to a longitudinal axis of said support, in which method a substantially plane membrane is thermally welded to one end of said substantially cylindrical support substantially perpendicularly to said longitudinal axis of said support and, after cooling, said support is torn off said membrane in a direction substantially perpendicular to the plane of said membrane so that portion of said membrane substantially corresponding to said end of said cylinder remains welded to said support, in which a precut of the membrane is formed at the time of said thermal welding, enabling it to be torn without burrs and in which, after a support is welded to said membrane a suction plate is placed under said membrane and suction is applied substantially in the direction of said longitudinal axis of said support before tearing is executed.