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In designing future nanoscale devices or nanostructures as new element in structural mechanics, it is very important to predict the responses for these elements against various mechanical loading conditions. In this letter, an analytical solution of the impact response in double layer graphene sheets (DLGSs) is presented using a continuum mechanics theory. In this analytical model, the DLGSs are considered as a layer stack of two individual graphene sheet (GS) bound together by van der Waals (vdW) forces. The influence of impact velocity and mass on the impact response are predicted by using numerical simulation. The result shows that impact response of GSs subjected to nanomass has exceedingly short times with picoseconds order.