Improving the stability of antibodies for manufacture and shelf life is one of the main focuses of antibody engineering. One stabilization strategy is to perform specific mutations in human antibodies based on highly stable antibodies in other species. To identify the key residues for mutagenesis, it is necessary to understand the roles of these residues in stabilizing the antibody. Here, we use molecular dynamics simulations to study the molecular origin of the four shark immunoglobulin new antigen receptors constant domains (C1–C4). According to the unfolding pathways and the conformational free energy surfaces in 8 M urea at 380 K, the C2 domain is the most stable, followed by C4, C1, and C3, which agrees with the experimental findings. The C1 and C3 domains follow a common unfolding pathway in which the unfolding starts from the edge strands, particularly strand g, and then gradually progresses to the inner strands. Detailed structural analysis of the C2 domain reveals a “sandwich-like” R339-E322-R341 salt-bridge cluster on strand g, which grants ultrahigh stability to the C2 domain. We further design two sets of mutations by mutating E322 to alanine or setting all atomic charges in E322 to zero to break the salt-bridge cluster in the C2 domain, which confirms the importance of the salt bridges in stability. In the C4 domain, the D80-K104 salt bridge on strand g also strengthens the stability. On the other hand, in the C1 and C3 domains, there is no salt bridge on strand g. In addition to the salt bridges, the overall hydrophobicity score of the hydrophobic core is also positively correlated with the domain stability. Our findings provide a detailed microscopic picture of the molecular origin of the four shark immunoglobulin new antigen receptors constant domains that not only explains the differences in their structural stability but also provides important insights into future antibody design.