The periodic stripe domains of magnetic material whose easy axis is perpendicular to the film thickness may have boundary layer behavior not only in the wall but also near the film surfaces. This behavior is especially pronounced when the material characteristic length is much less than the film thickness. By means of direct minimization from a variational principle, the magnetization in the periodic stripe domains is determined numerically using a mesh scheme, in which the boundary layer behaviors in the wall and near the film surfaces are adequately represented. The results confirmed the boundary layer behavior a posteriori. The stripe width is, in general, dependent upon Q = K/2πM2. However, the dependence is quite insensitive when the material characteristic length/film thickness ratio is less than 0.1. The results were compared with those of the theory based on the Landau-Lifshitz wall energy density concept due to Málek and Kambersky. The comparison shows that the magnetostatic energy density is substantially lower in contrast to the slight increase in the wall energy density defined as the sum of anisotropy and exchange energy densities.