A screw compressor or pump includes: a housing, two intermeshing rotors respectively rotatably mounted in the housing by two shafts; each rotor having a helix tooth spirally formed on the rotor lengthwise, with the helix tooth gradually decreasing an outer diameter of a top land surface of the helix tooth corresponding to a gradually contracted rotor chamber, and having a spiral groove juxtapositioned to the helix tooth and spirally formed in the rotor lengthwise; the spiral groove having a groove bottom surface extrapolatively defining an inner cone tapered towards a suction port side; the rotor chamber having a conical wall surface extrapolatively defining an outer cone tapered towards a discharge port side, thereby forming a gradationally contracted cavity between the spiral groove and the conical wall surface of the rotor chamber as confined between the inner and outer cones for increasing the compression or pumping efficiency.