In this paper, the authors propose, investigate, and discuss a concept of novel type of deployable helium-filled aerostat as a low-cost mean of transport. Internal construction of the aerostat is based on ultra-light tensegrity structure equipped with prestressed tensioned elements of controllable lengths. Such tensegrity structure allows for adaptive morphing of the aerostat understood as simultaneous controllable modifications of aerostat volume and shape during the flight. The controlled volume changes enable influencing buoyancy force and obtaining desired vertical motion during the ascending and descending process. In turn, external shape changes allow for lowering the aerodynamic drag and energy usage needed to uphold stable horizontal position or maintain the desired flight path. Moreover, such internal structure allows for convenient storage, transportation and deployment of the aerostat construction on the ground or in required point at the atmosphere. The article presents an analysis of the exemplary operational mission of the aerostat. The authors introduce the mechanical model capturing interaction of the internal tensegrity structure and aerostat envelope based on the finite-element method, as well as dynamic model allowing for simulation of the aerostat’s vertical and horizontal motion influenced by buoyancy and drag forces. Both these models are used to positively verify the feasibility of the proposed concept of deployable tensegrity-based aerostat with adaptive morphing and its efficiency in realization of the assumed flight mission.