One of the promising directions in the framework of the concept of creating the next-generation 5G/IMT-2020 networks is the development of broadband wireless networks based on autonomous unmanned aerial vehicles (UAVs). In addition to the interest in autonomous UAV-based high-altitude platforms (HAPs), leading researchers are currently engaged in the design and implementation of tethered unmanned HAPs, which are intended to be long-term operating and are widely used in civilian and military areas. Their possibility of long-term operation, which is one of the main advantages over autonomous UAVs, puts forward new reliability requirements. In this paper we study an analytical reliability model of the multi rotor flight module of the tethered HAP as a homogeneous hot-standby system consisting of $n$ elements operating in a random environment. A general Markov reliability model of the considered system operating in a random environment is proposed, which accounts for the increase in the functional load and the location of the failed components.