A nonlinear von Kármán-type model of nano-plate bending was formulated incorporating the surface elasticity of Gurtin–Murdoch and basing on the Kirchhoff hypothesis. Unlike most of previous related theories, surface tension was taken into account with quadratic terms equal to the von Kármán-type strains. Besides, it was shown it is surface tension, incorporated in bending equation, that is responsible for the conjugation condition of Young–Laplace law in the transverse direction, which until recently has been usually omitted or indirectly satisfied. The example of solving a nonlinear one-dimensional problem illustrated the effect of surface tension on bending, free transverse vibrations, and compressive buckling of a nano-plate.