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Derivation of analytical expressions for research and development of sensors for monitoring the state of track sections with current track receivers. To achieve this goal, it is proposed to consider the sensors for monitoring the state of the track sections with power supply in the middle of the rail line, and to connect the receivers inductively to the rail line at the ends of the control sensors. The derivation of the basic equations was carried out using the theory of four-terminal and the theory of electrical circuits with the representation of control sensors in the form of equivalent circuits, by which the coefficients of the rail four-terminal of the main control sensor were determined at the initial stage. On the basis of which the equations of absolute shunt sensitivity and the criterion of sensitivity to the normative shunt were then derived. As a result of the work, analytical expressions were determined to determine the current flowing over the inductive coils, as well as the values of the absolute shunt sensitivity and the sensitivity criterion for the standard shunt for monitoring sensors with current track receivers. A method is proposed for deriving analytical expressions for research, development, and design of jointless control sensors with current receivers.The proposed method for monitoring the state of track sections using jointless control sensors with current receivers allows us to provide a clear boundary for fixing the entrance and exit of trains from the controlled section, regardless of fluctuations in the resistance of the ballast of the rail line and thereby increase the safety of train traffic.