The effects of lateral surface mass transfer on the natural convection boundary layer about a vertical plate fin with solution-determined thermal boundary conditions (or fin temperature distributions) in a fluid-saturated porous medium were studied numerically. It was found that the governing parameters far the problem are the convection-conduction parameter Nccand the lateral mass flux parameter fw. The non-similar solutions were obtained by the local nonsimilarity method and were carried out up to the third level of truncation. The effects of mass flux on fin temperature distribution, boundary-layer thickness, local heat transfer coefficient, local heat flux, and total heat transfer rate are presented and discussed.