Intimate relationships between the structure and the mechanical properties of polymer crystals are discussed from the molecular theoretical point of view. (1) The Young’s modulus along the chain axis is dependent largely on the molecular conformation and the force constants. Some typical polymers including polyethylene, polyoxymethylene, poly(p-phenylene benzobisoxazole) and cellulose are discussed. (2) Three-dimensional anisotropy of the Young’s modulus is discussed in relation to the packing mode of the chains. In the case of isotactic polypropylene crystal, the important role of anharmonic torsional vibrational modes of the methyl groups is discussed, which significantly governs the anisotropy of the elastic constants. (3) The molecular deformation mechanism was predicted lattice-dynamically and proved experimentally on the basis of vibrational spectroscopic measurements. The direct experimental evaluation of the theoretically predicted atomic displacements was performed for the first time through the refined X-ray structural analysis of polydiacetylene single crystal under the application of tensile stress. (4) The molecular design of novel polymer materials with three-dimensionally high Young’s moduli is made starting from the various types of conventional polymer crystals such as poly(p-phenylene benzobisoxazole), polyacetylene, poly(p-phenylene), orthorhombic polyethylene and cellulose. Some of these crosslinked polymer crystals were found to possess a Young’s modulus exceeding that of diamond crystal.