An in-line capillary rheometer nozzle equipped to a conventional reciprocating 55-ton injection molding machine was used to study the viscosity of single phase low density polyethylene (LDPE)/chemical blowing agent (CBA) solutions under high shear rate in the concentration range of 0 to 5 wt%. The steady shear viscosity of LDPE with endothermic and exothermic chemical blowing agents was measured for shear rates ranging from 170 to 200,000 s(-1) and under pressure conditions up to 36 MPa. Pressure-volume-temperature (pvT) measurements were determined to account for the pressure effects and the changes of the free volume during processing. The viscosity reduction of the polymer-CBA solution was found to be dependent on the concentration of the chemical blowing agent and melt pressure. A model based on a simplified Cross-Carreau model, incorporating the pvT behavior of LDPE, and the free volume concept was proposed to estimate the viscosity reduction resulting from the addition of a chemical blowing agent. The model employs a scaling method based on concentration-dependent and pressure-dependent shift factors to collapse the viscosity measurement to a master curve at each temperature.