A mathematical model is presented for solids deposition from multicomponent "waxy" mixtures under laminar flow in a small double-pipe heat exchanger. The model is based primarily on the moving boundary problem approach involving heat transfer with a phase change. A novel formulation based on the one-dimensional deformation of a cubical cage is proposed for incorporating the effect of shear stress on the deposition process. It is postulated that the application of shear stress causes tilting of the cubical cage, which leads to the release of a portion of the liquid phase. The tilted-cage deformation angle is estimated by matching the deposit-layer composition data from two recent experimental studies. A change in the deformation angle is predicted to result in a shift in the carbon-number distribution of the deposit. The shear stress is predicted to cause a wax enrichment of the deposit layer without affecting the deposit-layer thickness, which is governed mainly by heat-transfer and phase equilibrium considerations. The estimated deformation angle is shown to depend upon the fractional deposit thermal resistance (or the fractional temperature drop), deposit mass, and Reynolds number. The results of this study confirm that the deposition process is primarily thermally driven, while the deposit composition is influenced by shear stress and thermodynamic considerations.