This　paper　studies　an　inverse　design　problem　of　a　general　eigenvalue　of　a　dynamic　system　where　the　elements　of　the　rigidity　and　mass　matrices　are　linear　with　respect　to　a　design　vector　b.　The　coefficients　of　spring　and　mass　of　a　lumped　parameters　structure,　the　length　and　width,　the　radius,　etc　play　the　role　of　design　parameters.　For　some　specified　eigenvalues　and　eigenvectors,　the　design　parameter　vector　can　be　obtained　and　the　rigidity　and　mass　matrices　of　an　initially　designed　structure　can　be　reconstructed　by　solving　linear　algebra　equations.　The　theory　and　method　can　not　only　be　used　for　an　in-line　system,　but　it　can　also　be　used　for　an　inverse　vibration　design　of　a　complex　structure.