The problems of hydrostatics and hydrodynamics of a liquid subject to gravity forces and surface tension are of interest in connection with the study of liquid behavior in weak gravity fields and under conditions of weightlessness. The present paper considers the problem of determining the equil ibrium form of a liquid in a vessel in the presence of gravity forces and surface tension, This problem has been considered previously for axisymmetr ic vessels in [1, 2]. The asymptotic solution of the problem of liquid equilibrium in a vessel of arbitrary form in the case when the gravity forces are large in comparison with the surface tension forces was obtained in [3]. Some resuks on the equilibrium problem are presented in [4]. In the present paper we use the variational approach to the equil ibrium problem [3, 4]. Certain properties of the variational problem for this case are proved which make it possible to use direct methods for its solution. For the numerical solution of the problem we use the method of local variations presented in [5]. This method permits obtaining the solution for vessels of arbitrary form. The results of calculat ions for vessels in the form of a rectangular parallelepiped are presented.