Some intrinsic properties of biomaterials are calculated with atomistic computer simulations through energy minimizations and molecular dynamics methods. The mechanical properties of bulk polymers such as poly(vinyl alcohol) and poly(ethylene terephthalate) are obtained in terms of the Young's modulus, the bulk and shear moduli, and the Poisson ratio below the glass transition temperature. The calculated values apply to an ideal, defect-free sample, and therefore, they correspond to the theoretical upper limit for the mechanical behavior of these materials. The surface hydration of the same polymers and of graphite is analyzed in terms of the statistical distribution of the water molecules near the surfaces of these materials that range from hydrophilic to strongly hydrophobic. Consistent with recent spectroscopic evidence, it is found that water forms relatively ordered hydration shells driven by hydrogen bonds above the hydrophilic surface, but is highly disordered over the hydrophobic one. Therefore, it is suggested that computer simulations provide a new useful tool to investigate various aspects of biomaterials.