The grand canonical Monte Carlo (GCMC) simulation method has been used to estimate the disjoining pressure and to obtain the distribution of the density of the adsorbed Lenard-Jones fluid in finite narrow slits between nanosized surfaces of graphite. The influence of the radius of the cross section of the slit and the chemical potential on the properties has been considered. Different contributions from fluid-fluid, fluid-solid and solid-solid interactions to the solvation force have been analyzed. Significant effects of the chemical potential are observed for the finite slits. The oscillatory behaviour of the mean density and the disjoining pressure depends on the width of a finite slit is similarly to this of an infinite slit. A decrease of the chemical potential leads to some reduction of absolute values of the disjoining pressure and the mean density. Edge effects are exhibited in larger values of the local pressure on the central area of the finite slit than on its periphery. The toroidal region with a high concentration of the adsorbed fluid appears out of the slit near its edge. Predictions of the asymptotic theory for finite slits in equilibrium with liquid fluid phase have been confirmed.