A dilute polymer solution is modeled by linear and nonlinear dumbbells suspended in a Newtonian solvent. The Langevin equations governing the motion of the dumbbells in the tube are solved with the help of Brownian dynamics simulations consistent with the momentum balance equation. To this purpose a previously presented consistent numerical approach has to be specialized to tube flow. The models show typical features as the slip effect, the flow enhancement, and the reduction in viscosity with decreasing tube radius.