Structures of typical low index surfaces, {100} and {110}, of an n-alkane crystallite made up of 400 molecules are investigated by Monte Carlo simulation. Each molecule in the crystallite is assumed to be rigid and to make rotation and translation about the chain axis as well as transverse displacement from the reference lattice point. The structure and molecular mobility at each surface, and their temperature dependence, are studied as a function of depth from the surface. In a fully ordered state at lower temperature, where the crystallite has the usual herringbone structure, the molecules near the surfaces also pack in a similar herringbone structure. The increase in temperature gives rise to very pronounced disorders at the surface regions of two or three molecular layers, especially at the {100} surface, besides overall disordering in the crystallite. The surface disorder is found to be characterized by the loss of the typical herringbone structure and the enhanced translation of the chain; these features are shown to be characteristic of the rotator phase RI of an n-alkane. The significance of such disordered surface structures in the crystal growth theory is discussed.