This study is concerned with the effects of nanotubes' alignment in the buckypaper on the overall mechanical properties of a buckypaper polymer matrix nanocomposite. Alignment of single-walled carbon nanotubes (SWNTs) in buckypapers was achieved by filtration of singlewall nanotube suspension through a filter placed in a high strength magnetic field. We have investigated the role of nanotubes' alignment in effective elastic properties of a buckypaper nanocomposite. Orientation distribution of nanotubes was measured using SEM images and image processing software. A simple micromechanical model that includes prescribed orientational dependence and anisotropy of inclusions is proposed. Its validity in the context of rigorous classical bounds is discussed. The modeling results are also compared with the experimental ones.