Substantially constant tension is maintained on a melt-blown nonwoven fibrous sheet by mounting the sheet take-up roller for longitudinal movements relative so as to accommodate the increasing diameter of the sheet material being wound convolutely on the take-up roller. Sheet tension during production is thereby maintained substantially constant by virtue of a continual increase in the longitudinal distance (in relation to the machine direction) between the fiber collection mandrel and the take-up roll. Preferably, tension control is achieved by a pneumatic pressure-regulating system which includes at least one rotatable press roller which is longitudinally fixed in position relative to the collection mandrel and is in contact with the sheet material being wound around the take-up roll. The take-up roller is pneumatically advanced toward the press roller by the pneumatic actuation of at least one air cylinder. Thus, as the diameter of the sheet material being wound around the take-up roll increases, the pneumatic ram of the air cylinder will cause the pneumatic pressure of the air cylinder to correspondingly increase. This increase in pneumatic pressure is sensed by a pneumatic pressure regulator which vents sufficiently to decrease the pneumatic pressure acting on the air cylinder to a predetermined set point pressure. In this manner, the pressure exerted on the sheet material between the positionally fixed press roller and the longitudinally movable take-up roller is maintained substantially constant during production of the nonwoven sheet material.