The hypothesis of a sequence of architectural mastering of the moon suggests several stages of settlement. At the first stage, it is necessary to deliver and build light structures for the cosmonauts of the "pioneers". The requirements for a constructive, technological and planning solution of such first lunar "tents" are revealed. Issues of spatial rigidity and stability of forms under conditions of lunar gravity are investigated. The analysis of lightweight and pre-fabricated systems led to the choice of two options, having a very compact form in the assembled state and quickly unfolding at the construction site. The authors of these designs are Russian engineers and architects. The first lunar buildings should use the lunar soil as a thermal insulation and anti-radiation protection. According to the hypothesis, the second stage of the architectural and constructive exploration of the moon is assumed. At this stage modular buildings will be erected for living, research and production. They can be stationary and mobile. Different design solutions of such buildings are analyzed. Conclusions about the feasibility of the use of certain structures. © 2020, Univelt Inc. All rights reserved.