Molecular transport under the conditions of single-file diffusion was investigated near the channel boundaries by using dynamic Monte Carlo and molecular dynamics simulations of tracer exchange between single-file channels and their surroundings. The boundary effect reported in our recent papers (Vasenkov S.; Kärger, J. Phys. Rev. E 2002, 66, 052601. Schüring, A.; Vasenkov S.; Fritzsche, S. J. Phys. Chem. B 2005, 109, 16711) was studied in detail. This boundary effect is characterized by deviations of the intrachannel concentration profiles of tracer molecules observed in the case of single-file diffusion near the channel boundaries from the corresponding profiles typical for normal diffusion. It has been shown in our previous studies that these deviations occur under the conditions when the potential-energy difference inside and outside of single-file channels was both comparable and much larger than the activation energy of intrachannel diffusion. Here, we report a quantitative model describing the boundary effect. According to this model, an occurrence of the boundary effect is related to a complex character of diffusion in finite single-file systems. Such diffusion can be described by the following two types of movements occurring in parallel: (i) correlated displacements of all molecules in any particular channel and (ii) fast displacements of single molecules, which are uncorrelated with the displacements of all other molecules in the same channel. The latter displacements are restricted to a certain length interval that depends on the channel length and the channel occupancy. This length interval is shown to determine the extensions of the channel margins where the boundary effect is observed.