A continuous extrusion process for the manufacture of low-density, microcellular foams is presented. Microcellular polymers are foamed plastics characterized by a cell density greater than 10⁹ cells/cm³ and a fully grown cell size on the order of 10 μm. Previous research on the continuous processing of microcellular polymers has focused on the control of microcell nucleation in extrusion. This thesis presents an effective means for the control of cell growth by freezing the foam skins in order to achieve a desired expansion ratio in microcellular foam processing that uses CO₂ as a blowing agent, a means of lowering the melt temperature to prevent deterioration of the cell-population density via cell coalescence, and a means of employing lubrication to suppress the melt fracture observed on the extruded foams. Promotion of a desired volume expansion ratio and prevention of cell coalescence while suppressing the melt fracture in microcellular foam processing were experimentally verified. The influences of processing parameters such as melt temperature, nozzle temperature, amount of injected CO₂, and amount of injected lubricant on the final foam morphologies were investigated. By tailoring the extrusion processing parameters, microcellular HIPS and HDPE foams with a cell density of 10⁸-10¹⁰ cells/cm³ and a controlled expansion ratio in the range of 1.5 to 25 were successfully obtained.