The results of the numerical analysis of a mathematical model for a single bubble dynamics are presented. In the model, one studies the effect of macromolecular polymers additives on the cavitation generated by a variable acoustic wave in a viscoelastic liquid. On the basis of the numerical analysis, it is found out that the polymer additive weakens the phenomenon of cavitation, which is shown on the characteristics presenting the damping effect of the polymer additive on a single bubble.