A floating fish production system for placement within a body of water and being structured and disposed for containing fish and other aquatic animal, plant and algal species, the system including at least one primary containment tank having an arrangement of individual solid wall sections and an arrangement of individual solid floor sections. Flexible membranes span between and connect to adjacently positioned solid wall and floor sections to define flexible connecting joints that allow the individual solid wall and floor sections to move relative to one another in an articulating action. The flexible membranes allow the tank configuration to temporarily deform from a relaxed state in response to externally applied forces exerted on the tank (e.g., waves, wind, current) to thereby absorb the externally applied forces and reduce stress on the structural integrity on the tank. An air lift system including a high volume, low pressure blower and a spaced arrangement of vertically extending air lift pipes delivers water and oxygen from the exterior body of water and into the tank interior. A flexible main drain in a central area at the bottom of the tank connects to a waste recovery system for removing waste produced by the fish and other aquatic species.