This invention relates to multi-shaft screw extruders in which the screw shafts are arranged to intermesh in pairs and rotate pairwise in the same sense, each shaft of a pair having at least one double threaded or triple threaded pressure build-up section corresponding to that of the other shaft. This invention also relates to a method of using such an extruder to build up pressure within a material with a minimum pressure build-up section and a minimum power input. The extruder and its method of operation are characterized by the fact that at least a portion of the pressure build-up section satisfies ##EQU1## WHEREIN T IS THE SCREW PITCH, D IS THE INTERNAL DIAMETER OF THE HOUSING, Q IS THE VOLUMETRIC THROUGHPUT OF MATERIAL OF A SCREW PAIR AND N IS THE SPEED OF ROTATION OF THE SCREW SHAFTS AND: ##EQU2## WHEREIN IN TRIPLE THREAD PRESSURE BUILD-UP SECTIONS A = 0.1082;a = 15.316;b = 69.111;Andc = 261.85And in double thread pressure build-up sectionsA = 0.206;a = 8.8212;b = 18.414;Andc = 31.668.