We study the buoyancy-driven motion of two-dimensional bubbles and droplets in a Bingham fluid using a regularization method. The finite-element computations are carried out using the method of level sets to track the interface. We find that multiple bubbles and droplets can move in a body force field under conditions where a single bubble or droplet with the same physical properties would be unable to overcome the integrated yield stress and would be trapped. The finite yielded region around a single bubble or droplet in a Bingham fluid causes a backflow, resulting in unyielded “ears” that rotate and exchange material points with the yielded fluid to maintain a fixed position on the equatorial plane as the bubble rises or the droplet falls. The backflow flattens the tail of the trailing bubble or droplet in a pair and, at a sufficiently high level of interfacial tension, causes a splitting of the tail and the creation of a cusp. Three bubbles in a triangular configuration interact in a manner that is qualitatively predictable by considering pair interactions. Despite important differences in detail, the general shape evolution of bubbles and droplets in a Bingham fluid is similar to that in a Newtonian liquid when time scales are considered on a comparable basis.