By means of vibrational spectroscopy, the study examines the structure of matrix materials synthesized through the quenching of sodium-rubidium aluminoborosilicate melts with the addition of zirconium. Zirconium was found to have a significant effect on the ratio of the main structural units and the distribution of modifier cations among them in the glass structure. The obtained results were used to explain changes in the glass-melt transition temperature and synthesized material density; they can be useful in adjusting the composition and synthesis parameters of matrix materials for the immobilization of high-level radioactive waste containing significant amounts of zirconium.