The advantage of using resonant sonic mixers in industrial applications is that it makes the mixing of fluids more efficient. Factors such as the operation of resonant frequencies and the generation of sound waves of suitable amplitude with significant acceleration play a major role in homogenizing the mixture in the shortest possible time and distinguish this technology from other mixing processes. In the case of viscoplastic resins, mixing of solid particles is a common problem. In such systems, the presence and movement of gas bubbles significantly affect the flow dynamics and the uniformity of the mixture. In essence, the motion and deformation of bubbles reveal new dimensions in mixing indicators, which are crucial for designing uniform mixing in polymer applications. Accordingly, this research investigates the dynamic behavior of vertically aligned bubble pairs in viscoplastic fluids under vibration, while also examining the impact of rheological parameters on hydrodynamics and the likelihood of resonance occurrence for these bubble pairs. The results indicate that increasing the yield stress, along with the consistency and flow behavior indices of the fluid, leads to higher apparent viscosity and reduced shear-thinning properties, thereby decreasing the ascent velocity of the bubbles. Consequently, this results in an increased drag coefficient and longer ascent time for the bubble pair. Furthermore, as fluid viscosity rises, the transfer of vibrational energy to the system diminishes, leading to a pronounced phase lag in the response of the two-phase system (comprising the fluid and bubble pair).