Abstract: A thin layer of the event horizon vicinity under the two-dimension black hole spacetime with a global monopole is considered as a system of the Casimir type.The energy-momentum tensor is derived in Boulware vacuum,Hartle-Hawking vacuum and Unruh vacuum respectively.The values are derived in the massless scalar field which satisfies the Dirichlet boundary conditions.By the Wald’s axioms,the result is the same with one by the usual regularized methods.Meanwhile,energy,energy density,and pressure acting on Dirichlet walls at the asymptotically flat background are also calculated.According to the energy,the Casimir force is derived.