A numerical method is implemented for computing the shape of a three-dimensional hydrostatic meniscus extending between two arbitrary closed contact lines under the restriction that the projections of the contact lines in a horizontal plane are eccentric circles. In a physical realization, the contact lines are attached to vertical circular cylinders, spherical particles or containers. The Laplace-Young equation determining the meniscus shape is solved in bipolar coordinates generated by conformal mapping using a finite-difference method, and the capillary force and torque exerted on the cylinders are evaluated. Numerical results are presented for a meniscus extending between two circular horizontal contact lines. The horizontal component of the capillary force at each contact line is found to increase monotonically with the cylinder center offset, favoring the concentric configuration. (C) 2010 Elsevier Inc. All rights reserved.