A mathematical model based on the moving boundary problem formulation for solids deposition was modified to account for the effect of shear stress in laminar flow of paraffinic mixtures. The effect of shear stress on the composition and growth of the deposit layer was incorporated via a recently proposed approach involving one-dimensional deformation of a cubical cage, leading to the release of a fraction of the liquid from the deposit. Numerical solutions were obtained for the growth of the deposit layer with time, both radially and axially. Predictions were obtained for the effect of different cubical-cage deformation angles on the composition and solid/liquid phase ratio in the deposit layer. Whereas an increase in the deformation angle was predicted to cause wax enrichment in the deposit, the deposit-layer thickness was primarily dependent upon the heat-transfer and phase equilibrium considerations. The predictions also indicated that an increase in the deformation angle delayed the deposition process, because of a corresponding increase in the average solid-phase fraction within the deposit, and it caused the deposit to become enriched in heavier n-alkanes and depleted in lighter n-alkanes.