Yield stress materials containing a dispersion of small inclusions represent a widespread spectrum of advanced materials and are found in all scales of natural systems and industrial processes. The dynamics of such systems received only limited attention so far. We have studied the motion of single and interacting drops and bubbles in a yield-stress fluid which was contained in long cylindrical vessels by optical observations. The motion of the dispersed particles is induced by gravity. The parameters varied were critical stress of the ambient phase, drop and bubble sizes, and cylinders diameters. We report critical conditions for motion, migration velocity, droplets and bubbles deformation patterns, drops interaction dynamics including separation and coalescence, and visualization of streamline patterns in the yielded regions of axi-symmetric motion via PIV technique.