Abstract: A truss vibration optimization problem is to minimize the total weight of truss subject to a given fundamental vibration frequency. This paper focuses on the recent results of matrix algebraic approach to solve the truss vibration optimization problem expressed in terms of symmetric semidefinite programming problem. We derive two sufficient conditions on constructing the symmetric group representation to reduce the problems size. An example of eight-bar truss design problem is given to illustrate how to construct a group representation and to demonstrate its effectiveness.