The aim of this research is to create a mechanical and mathematical model of a multi-rod stabilizer for the sport archery bow and to analyze its capability to damp disagreeable recoil and vibration of the bow during internal ballistic motion. The research methods are based on the Euler-Bernoulli theory of beam bending, Lagrange equations of the second kind, the Cauchy problem, and the Runge-Kutta method. A mathematical software package was used to analyze the problem. The approach to the problem of sport-bow stabilization in the vertical plane that is proposed in this paper addresses the practical needs both of applied engineering mechanics and of the sport of archery. Numerical results from computer simulation are presented in both tabular and graphical form. The common motion of the string and arrow (internal ballistic motion) is accompanied by intense vibration which is caused by disruption of the static force balance at the moment of string release.