The subject of the present theoretical study is the dynamics of bubble-bubble interactions in a viscoelastic medium. First, new equations for calculating the viscoelastic drag exerted on bubbles during their translational motion in a viscoelastic medium are derived. The drag equations are incorporated in the bubble-bubble interaction model in which, thereby, both the translational and radial motions of the bubbles are affected by the viscoelastic features of the medium. Second, the derived equations are applied to investigate how the viscoelastic properties of the medium can affect the dynamics of multiple bubbles, as well as how the bubbles can affect each other. It was discovered that the bubble-bubble interaction can significantly influence the dynamics of a single bubble. As the distance between the bubbles increases, their effect on each other decreases, and at a distance of several millimeters, this effect can be neglected. Moreover, it was concluded that with increasing elasticity and viscosity of the medium, as well with decreasing relaxation time, the effects of other bubbles on the current bubble's radial motion can become negligible. The translational motion of the bubbles was investigated for different viscoelastic models. The elasticity resists the motion of bubbles in space, resulting in a dynamical steady state of the distance between the bubbles at high elasticity values. The relaxation time of the medium was also found to be important in terms of the bubbles' translational movement.