The axisymmetric dynamics of single and interacting deformable fluid inclusions in yield stress fluid are investigated. The drops move in a cylindrical tube under the action of gravity. The velocities of the drops, deformation patterns, and the evolution of yield domains were examined for a variety of physical parameters including the interfacial tension, the yield stress, and the geometry of the system. Particular attention is given to the evolution of the yielded regions in the ambient matrix and to the deformation of the interfaces of the inclusions. The results of simulations show that, for a single drop, a quasistationary state is established after a relatively long transient period. The interaction of two drops results in a substantial extension of the yielded domain and in the acceleration of the motion. Two equal-size drops tend to approach each other and coalesce. Afterward, a single large fluid particle is formed that sometimes breaks up forming one large leading drop and one or several small trailing satellites.