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