In this paper we deal with the problem of the generation of internal waves at the bottom of convective zone in solar-type stars, and with the transport process linked to the non-adiabatic propagation of these waves through the stable radiative region. The main improvement with respect to the previous papers in this series comes from the convection treatment chosen in order to describe the perturbations exciting the internal waves at the boundary convective/stratified zones. We consider a model of convective transport by plumes as described by Rieutord & Zahn (1995), taking into account the presence of overshooting as modelled by Zahn (1991). A model of convective transport by plumes implies that it is no longer necessary to introduce an ad hoc parameter to emulate the consequences of asymmetric downward and upward flows, as was the case when a classical description of the convection was adopted. The velocity field produced in the stellar interior by gravity waves provides a diffusion coefficient. The predictions of this transport process for light element abundances in low-mass stars reproduce the observational features of lithium abundance: its dependence on mass and age. Furthermore, a phenomenological treatment of the interaction rotation/overshooting based on numerical simulations of the penetrative convection with and without rotation (Julien et al. 1996a, 1997a) provides a more or less efficient mixing process depending on the rotational state of the star and reproduces the observed ``correlation'' between lithium abundance and rotational velocity and the scatter of lithium abundance in stars of the same age, mass and chemical composition. The dependence of the diffusion coefficient on the depth below the convective zone is tested by comparing the prediction for Be abundance with the available observations. The results are also in good agreement, but the uncertainties in the observations are too large.