Natural 2'-modified nucleosides are the most widely used antiviral therapy. In their triphosphorylated form, also known as nucleotide analogues, they target the active site of viral polymerases. Viral polymerases have an overall right-handed structure that includes the palm, fingers and thumb domains. These domains are further subdivided into structurally conserved motifs A-G, common to all viral polymerases. The structural motifs encapsulate the allosteric/initiation (N1) and orthosteric/catalytic (N2) nucleotide-binding sites. The current study investigated how nucleotide analogues explore the N2 site of viral polymerases from three genera of the family Flaviviridae using a stochastic, biophysical, Metropolis Monte Carlo-based software. The biophysical simulations showed a statistical distinction in nucleotide-binding energy and exploration between phylogenetically related viral polymerases. This distinction is clearly demonstrated by the respective analogue contacts made with conserved viral polymerase residues, the heterogeneous dynamics of structural motifs, and the orientation of the nucleotide analogues within the N2 site. Being able to simulate what occurs within viral-polymerase-binding sites can prove useful in rational drug designs against viruses.