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We use in silico modelling of the SARS-CoV-2 spike protein and its mutations, as deposited on the Protein Data Bank (PDB), to ascertain their dynamics, flexibility and rigidity. Identifying the precise nature of the dynamics for the spike proteins enables, in principle, the use of further in silico design methods to quickly screen for existing and novel drug molecules that might prohibit the natural protein dynamics. We employ a recent protein flexibility modelling approach, combining methods for deconstructing a protein structure into a network of rigid and flexible units with a method that explores the elastic modes of motion of this network, and a geometric modelling of flexible motion. Our results thus far indicate that the overall motion of wild-type and mutated spike protein structures remains largely the same.