The SARS-CoV-2 Spike protein needs to be in an open-state conformation to interact with ACE2 to initiate viral entry. We utilise coarse-grained normal mode analysis to model the dynamics of Spike and calculate transition probabilities between states for 17081 variants including experimentally observed variants. Our results correctly model an increase in open-state occupancy for the more infectious D614G via an increase in flexibility of the closed-state and decrease of flexibility of the open-state. We predict the same effect for several mutations on glycine residues (404, 416, 504, 252) as well as residues K417, D467 and N501, including the N501Y mutation recently observed within the B.1.1.7, 501.V2 and P1 strains. This is, to our knowledge, the first use of normal mode analysis to model conformational state transitions and the effect of mutations on such transitions. The specific mutations of Spike identified here may guide future studies to increase our understanding of SARS-CoV-2 infection mechanisms and guide public health in their surveillance efforts.