The process of gas dispersion in the mixing zone of an extruder employing on-line injection into a viscous polymeric melt, has been analyzed. In the model system considered, the gaseous component was injected into a non-Newtonian melt (LLDPE) via a permeable wall, during which a shear field was imposed at right angles to the direction of flow of the melt. The dispersion of the injectant has been quantified in terms of the spatial coordinate positions of the microvoids as they travel through the melt. Computer simulation was performed to ascertain the trajectories, radial velocities, and times of traverse of the particles migrating from the injection orifice under the imposed shear field. Numerical solutions have been obtained for system angular velocity from 6 to 10 rad/s, melt viscosity from 6 to 6.5 kPa.s, particle diameter/ annular gap ratio of 0.20, injectant/melt density ratio of 0.032, and power law index of 0.51. The computed trajectories were found to be consistent with previously recorded visual observations. The analytical results on the time of traverse (∼0.5–1.0 s) indicated that dispersion by on-line shear injection was viable. The latter results, however, need experimental verification.