In this paper, we consider the following viscoelastic equations � u tt − � u + � t 0 g(t − τ)� u(τ)dτ + ut = a1|v| q+1 |u| p−1 u vtt − � v + � t 0 g(t − τ)� v(τ)dτ + vt = a2|u| p+1 |v| q−1 v with initial condition and zero Dirichlet boundary condition. Using the concavity method, we obtained sufficient conditions on the initial data with arbitrarily high energy such that the solution blows up in finite time.