When a drop of liquid wets two identical solid spheres, the liquid forms a capillary bridge between the spheres to minimize surface energy. In the absence of external forces, these bridges are typically assumed to be axisymmetric, and the shape that minimizes surface energy can be calculated analytically. However under certain conditions, the bridge is axisymmetrically unstable, and migrates to a non-axisymmetric configuration. The goal of this paper is to characterize these non-axisymmetric capillary bridges. Specifically, we numerically calculate the shape of the capillary bridge between two contacting spheres that minimizes the total surface energy for a given volume and contact angle and compare to experiments. When the bridge is asymmetric, finite element calculations demonstrate that the shape of the bridge is spherical. In general, the bridge shape depends on both volume and contact angle, yet we find the degree of asymmetry is controlled by a single parameter. (C) 2015 Elsevier Inc. All rights reserved.