This study presents an analytical flow model for the screw pump and compares it with the numerical simulations for the lubrication system of a variable speed hermetic reciprocating compressor used mainly in household refrigerators. Since variable capacity compressors (VCC) can be operated at different rotational speeds, a sufficient lubrication is required even at low rotational speeds where centrifugal effects are at a minimum. The lubrication system of such compressors includes a screw pump inside their crankshaft for this purpose. Using the analytical flow model, effects of the main design parameters for the screw pump to maximize the mass flow rate of the lubricant released from the upper part of the crankshaft are predicted and compared with numerical results. Specifically, the effects of the rotational speed, the oil viscosity, the submersion depth of the crankshaft in the oil sump and screw aspect ratio are investigated in this paper.