This work deals with the numerical modelling of hydrodynamics and mass transfer in developing laminar axial flow in an annulus. Complete momentum and mass conservation equations are solved by a finite element method using the FIDAP code. Concerning the diffusional problem. the results are in keeping with numerical predictions and experimental data available in the literature. We have particularly confirmed the fact that the axial velocity profile is characterized by velocity peaks in the vicinity of each cylinder of the annulus. This phenomenon is mainly due to the influence of the momentum longitudinal diffusion term. Resolution of the complete diffusion-convection equation allowed us to clarify the influence of the mass longitudinal diffusion term, neglected when using hypotheses of the boundary layer theory. The diffusion term must be taken into account for a correct prediction of the mass transfer in developing hydrodynamic and diffusional flow regimes.