The Irving-Kirkwood stress tensor has been calculated in spherical and infinite cylindrical cavities inside of an amorphous solid, with the cavities simulating pores of an adsorbent. The expressions obtained for the components of the stress tensor satisfy the conditions of mechanical equilibrium. The limiting behavior of the stress tensor under the conditions of a small curvature of the bounding surfaces coincides with the results of the asymptotic approach to the considered contribution from the solid surfaces.