In this paper, we consider the following Timoshenko equation $u_{tt}+\bigtriangleup ^{2}u-M\left( \left\Vert \nabla u\right\Vert^{2}\right) \bigtriangleup u+u_{t}=\left\vert u\right\vert ^{q-1}u$ associated with initial and Dirichlet boundary condition. We prove that the non-existence of solutions with positive and negative initial energy.