A linear autonomous nonconservative mechanical system is considered. The system smoothly depends on the parameter of a nonconservative load and on the vector of design parameters. The objective functional is dened as a minimal value of the nonconservative load parameter when the static or dynamic loss of stability takes place. The problem of finding the design parameters maximizing the objective functional is formulated. It is shown that such a problem of optimization is nonsmooth. The values of design parameters for which the objective functional discontinues are found. Necessary conditions of local extrema for such values are derived
