We numerically investigated the behavior of the water meniscus formed between a flat surface and a tip surface, which is flat or circular in shape, using the lattice Boltzmann method (LBM). The shape of the water meniscus formed between the flat bottom surface and the tip surface depends on the tip shape and the interaction between the water meniscus and the bottom or tip surface. The interaction is determined by the contact angles of the bottom and tip surfaces, resulting in different contact lengths between the water meniscus and the bottom or tip surface. The difference in these contact lengths depends on the effects of both the tip curvature and the interaction between the water meniscus and the bottom or tip surface. We classified the shapes of the water meniscus into seven different patterns as a function of the contact angles of the flat bottom and tip surfaces: concave, semi-concave, inverse semi-concave, column, convex, semiconvex, and inverse semi-convex.