The conditions of the two-phase liquid-vapor equilibrium of a Lennard-Jones fluid in thin unwetted slitlike and cylindrical capillaries of different widths were investigated at the temperature 90 K by the grand canonical Monte Carlo method. One of the main aims of this work was the estimation of the surface tension gamma for the curved meniscus (cylindrical and spherical). It is shown that the form of the dividing surface does not influence the dependence of gamma for a simple liquid on the curvature of this surface.