The article proves the equilibrium stability of hinged-rod system made of elastic material in pretension state for the case, when characteristics of some special matrix is not negative and certain amount of zero numbers concludes it. The author estimates the possible number of compression and tie bars of the system. The article identifies the number of parameters, the change of which allows fulfilling sufficient conditions of existence of the system under research.

Keywords: equilibrium stability, hinged-rod system, elastic material, topological construction, instantaneous lockstep, bracings.