In the present study, numerical simulations based on a two-dimensional two-phase lattice Boltzmann (LB) method have been performed to examine two types of capillary forces: (i) the lateral capillary force between two horizontal cylinders of wetting and/or non-wetting surfaces trapped at a liquid-vapor interface, and (ii) the capillary bridge force between the two wetting cylinders covered with liquid films in vapor. The force-distance profiles for these two systems agree well with those from the corresponding theoretical descriptions, indicating that the present LB simulation can reproduce the capillary forces between two bodies with various wettabilities.