© 2014, Pleiades Publishing, Ltd. Two local tangential and one nondiagonal components of the pressure tensor have been calculated inside circular plane-parallel empty slits with dispersion forces. Symmetric and asymmetric slits have been considered. The spatial dependences have the same character for both tangential components, although their absolute values are somewhat different. It has been shown that, in the symmetric slit, the corrections for its finite size to the tangential pressure appear to be larger than those to the normal pressure. The nondiagonal pressure component becomes noticeable only near the edges of narrow slits.