This article discusses the issue of selecting a pick system for cutting mining machinery, concerning the reduction of vibrations in the cutting system, particularly in a load-carrying structure at work. Numerical analysis was performed on a telescopic roadheader boom equipped with transverse heads. A frequency range of the boom’s free vibrations with a set structure and dynamic properties were determined based on a dynamic model. The main components excited by boom vibrations, generated through the process of cutting rock, were identified. This was closely associated with the stereometry of the cutting heads. The impact on the pick system (the number of picks and their arrangement along the side of the cutting head) was determined by the intensity of the external boom load elements, especially in resonance zones. In terms of the anti-resonance criterion, an advantageous system of cutting head picks was determined as a result of the analysis undertaken. The correct selection of the pick system was ascertained based on a computer simulation of the dynamic loads and vibrations of a roadheader telescopic boom.