An analysis is presented on how structural cores change shape within protein families, and whether or not there is a relationship between these structural changes and the vibrational modes that proteins experiment due to topological constraints. A set of 13 representative and well-populated protein families are studied. The evolutionary directions of deformation are obtained by applying a new multiple structural alignment technique to superimpose the structures and extract a conserved core, together with Principal Components Analysis (PCA) to extract the main deformation modes. A low-resolution Normal Mode Analysis (NMA) technique is used in parallel to study the properties of the mechanical core plasticity of the same proteins. We find that the evolutionary deformations span a low dimensional space. A statistically significant correspondence exists between these principal deformations and the vibrational modes accessible to a particular topology. We conclude that, to a significant extent, the structures of evolving proteins seem to respond to sequence changes by collective deformations along combinations of low-frequency modes. The findings have implications in structure prediction by homology modeling.