Abstract: A modular building unit is disclosed. The modular building unit includes at least nine elongated frame members, each forming one edge of a prism, which prism has at least three side faces and two end faces, with each end of each frame member being rigidly attached to an end of two other frame members. At least three parallel frame members include a channel running therethrough, which channel is open at both ends and adapted to receive a tensioning cable therethrough, whereby like modular building units can be held together at adjoining end faces by tensioning cables. Modular building systems for combining modular building units using tensioned cables are also disclosed.