A unique and novel SnO2 monolayer structure was introduced and studied by first-principles calculations based on the density functional theory (DFT). Bonding nature and band gap relation to elastic properties were obtained by fitting elastic energy as a function of Green-Lagrangian strain and calculating the elastic constants. The application of uniaxial strain produced a small in-plane stiffness with high Poisson’s ratio. These values revealed no lateral stress was resulted on bonds by the applied longitudinal strain. Area stiffness constant was defined for in-plane area expansion or compression. A higher area stiffness was found for biaxially placed strains, attributed to bending of the Sn-O-Sn bonds, which imposed a direct strain on the Sn-O bonds. Also, the electrons band gap varied from semiconductor energy at equilibrium atomic geometry to narrower gap with the application of biaxial strain. The variance was insignificant for the uniaxial strain case. We Show that the stability in the atomic bonding at strained conditions with fixed unit cell area gave controllability over the electronic state. Interlayer hybridization between O and Sn atoms made the band gap distinctly tunable with biaxial strain.