The article considers the stages of formation of the concept of stability, as well as the processes and elements that make up the concept of “sustainability of construction projects”.The authors propose to consider stability of construction projects as a reliability cube, each zone of which presents a space part. And the solution of the most practical problems requires only several zones, for instance, standard, risk and crisis ones, presented in a 3D coordinate system, where the abscissa axis will characterize the engineering stability, the ordinate axis – the functional stability and the z-axis - the financial stability.This approach allows us to use well-known and convenient mathematical instruments for the calculation of the probability of location of the project stability in the i-th state.