This paper presents a technology to determine the melt viscosity of a PS/supercritical CO2 solution using a linear capillary tube die mounted on a foaming extruder. CO2 was injected into the extrusion barrel and the content of CO2 was varied in the range of 0 to 4 wt% using a positive displacement pump. Single-phase PS/CO2 solutions were formed using a microcellular extrusion system and phase separation was prevented by maintaining a high pressure in the capillary tube die. By measuring the pressure drop through the die, the viscosity of PS/CO2 solutions was determined. The experimental results indicate that the PS/CO2 solution viscosity is a sensitive function of shear rate, temperature, pressure, and CO2 content. A theoretical model based on the generalized Cross-Carreau model was proposed to describe the shear-thinning behavior of PS/CO2 solutions at various shear rates. The zero-shear viscosity was modeled using a generalized Arrhenius equation to accommodate the effects of temperature, pressure, and CO2 content. Finally, the solubility of CO2 has been estimated by monitoring the pressure drop and the absolute pressure in the capillary die.