Vibration processes in the compound and open kinematical chain with an external link, as a model of an archery bow and arrow system, are evaluated. A mechanical and mathematical model of bend oscillations of the system during accelerate motion of the external link is proposed. Correlation between longitudinal acceleration and natural frequencies is obtained. There are recommendations regarding determination of virtual forms to study arrow vibrations and buckling. The models and methods have been adapted for realization into the engineering method using well-known mathematical software packages.