The stability of non-axisymmetric liquid bridges held between equidimensional coaxial disks of radius R and separated by a distance L is examined. The stability limits for lateral and axial acceleration are considered. The lateral acceleration stability limit is defined in terms of loss of stability by breaking. This limit is determined for both large and small values of the relative volume, V. The stability limit can be divided into two basic segments. One segment appears to be indistinguishable from part of the margin for the zero Bond number case. The other segment belongs to a one-parameter family of curves which, for a given Bond number and a fixed value of slenderness Λ= L/2R, have a maximum and minimum stable relative volume. The maximum volume stability limit tends to infinity as Λ→0. For any given lateral Bond number, the minimum volume stability limit is decreased and becomes indistinguishable from the zero Bond number limit when Λ becomes sufficiently small.