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Theoretical expressions are derived for calculating the capillary meniscus interactions between two vertical cylinders or two spheres partially immersed in a liquid layer. In general, the radii and the contact angles of the two particles can be different. Two alternative approaches are followed. The first one consists in calculation of capillary interaction energy, which is then differentiated to get the force. In the second approach the force is determined directly by integrating the pressure and the interfacial tension. A very good coincidence between the numerical results of these two independent approaches is established. The results can contribute to a better understanding of phenomena like surface aggregation, surface coagulation, and formation of two-dimensional arrays at interfaces.