The article is devoted to the relevant topic of more accurate selection of the design of the bottom-hole assembly (BHA) with a hydraulic test stand to create the necessary axial stress on the bit during drilling with coiled tubing rigs. A mathematical model of the BHA as a dynamic system with linear coefficients during longitudinal vibrations while drilling wells with a coiled-tubing system has been developed and analytically investigated. Analytical dependencies for determining the dynamic parameters of coiled-tubing BHA by a hydraulic test stand have been refined when operating in a directional well.