Prion diseases are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of mammalian species such as sheep and goats, cattle, deer and elk, and humans. But for rabbits, studies have shown that they have a low susceptibility to be infected by prion diseases. This paper does molecular dynamics (MD) studies of rabbit NMR structures (of the wild type and its two mutants of two surface residues), in order to understand the specific mechanism of rabbit prion proteins (RaPrPC). Protein surface electrostatic charge distributions are specially focused to analyze the MD trajectories. This paper can conclude that surface electrostatic charge distributions indeed contribute to the structural stability of wild-type RaPrPC; this may be useful for the medicinal treatment of prion diseases.