The high packing density inside proteins leads to certain geometric regularities and also is one of the most important contributors to the high extent of cooperativity manifested by proteins in their cohesive domain motions. The orientations between neighboring nonbonded residues in proteins substantially follow the similar geometric regularities, regardless of whether the residues are on the surface or buried, a direct result of hydrophobicity forces. These orientations are relatively fixed and correspond closely to small deformations from those of the face-centered cubic lattice, which is the way in which identical spheres pack at the highest density. Packing density also is related to the extent of conservation of residues, and we show this relationship for residue packing densities by averaging over a large sample or residue packings. There are three regimes: (1) over a broad range of packing densities the relationship between sequence entropy and inverse packing density is nearly linear, (2) over a limited range of low packing densities the sequence entropy is nearly constant, and (3) at extremely low packing densities the sequence entropy is highly variable. These packing results provide important justification for the simple elastic network models that have been shown for a large number of proteins to represent protein dynamics so successfully, even when the models are extremely coarse grained. Elastic network models for polymeric chains are simple and could be combined with these protein elastic networks to represent partially denatured parts of proteins. Finally, we show results of applications of the elastic network model to study the functional motions of the ribosome, based on its known structure. These results indicate expected correlations among its components for the step-wise processing steps in protein synthesis, and suggest ways to use these elastic network models to develop more detailed mechanisms, an important possibility because most experiments yield only static structures.