The theory of phase transitions on interfaces relates equilibrium vapor pressures and enthalpies of condensation. Since the latter are size-and shape-dependent properties and their variations are determined by variations of energies of autoadsorption on liquid menisci, a knowledge of these energies enable one to calculate the equilibrium pressures in capillaries. The novel mathematical model for a computation of the adsorption energies is developed on the basis of the Lennard-Jones potential for molecular interactions. The model is applied to hemispherical, conical, cylindrical, semi-elliptical, and paraboloidal menisci in nanocapillaries. Predicted equilibrium vapor pressures are favorably compared with the independent experimental data.