Numerical simulations of mass transfer into falling liquid films, both through the wavy interface and from the wall, have been performed for experimentally measured large waves within which the flow fields have been computed. Experiments have shown that the occurrence of waves on free falling films causes dramatic increases in mass transfer into the film, even under laminar flow conditions. Wave effects have been modeled in several ways, none of which predicts the observed rate of enhancement. The present numerical procedure includes solving the convective-diffusion equation for wavy films by extending a technique developed for hydrodynamic simulation. The presence of waves is shown to cause significant velocities normal to each interface. In conjunction with recirculation within the large waves, these flow patterns produce transfer rates for large waves that are several times larger than predicted for quasiparallel velocity fields. Experimental wave structure data were used to define the dimensions and frequency of an average large wave and surrounding substrate. Computed transfer rates at both the gas-liquid interface and the wall for a film composed of a periodic sequence of average waves agree well with published data. These simulations confirm the inadequacy of parabolic, or Kapitza-type velocity profiles in formulating transport models.