Identifying the fundamental cause of transmissibility of multiple mutation strains and vaccine nullification is difficult in general and is a source of significant concern. The conformational variability of the mutation sites for B.1.617.2 (Delta), B.1.617.1 (kappa), B.1.427/429 (epsilon), P.1 (gamma), B.1.351 (beta), B.1.1.7 (alpha), S477N, and the wild-type strain has been assessed using a deep neural-network-based prediction program of conformational flexibility or rigidity in proteins (SSSCPreds). We find that although the conformation of G614 is rigid, which is assigned as a left-handed (LH) alpha-helix-type one, that of D614 is flexible without the hydrogen bonding latch to T859. The rigidity of glycine, which stabilizes the local conformation more effectively than that of aspartic acid with the latch, thereby contributes to the reduction of S1 shedding, high expression, and increase in infectivity. The finding that the sequence flexibility/rigidity map pattern of B.1.1.7 is similar to that of the wild-type strain but is largely different from those of B.1.351 and P.1 correlates with the minor escape ability of B.1.1.7. The increased rigidity of the amino acid sequence YRYRLFR from the SSSCPreds data of B.1.427/429 near the L452R mutation site contributes to the 2-fold increased B.1.427/B.1.429 viral shedding in vivo and the increase in transmissibility relative to wild-type circulating strains in a similar manner to D614G. The concordance and rigidity ratios of multiple mutation strains such as B.1.617.2 against the wild-type one at the receptor-binding domain (RBD) and receptor-binding motif (RBM) regions provide a good indication of the transmissibility and neutralization escape ability except for binding affinity of mutation sites such as N501Y.