Pseudomorphic three-dimensional Ge nanocrystals (quantum dots) grown on thin silicon-on-insulator substrates can induce significant bending of the silicon template layer that is local on the nanometer scale. We use molecular dynamics simulations and analytical models to confirm the local bending of the Si template and to show that its magnitude approaches the maximum value for a freestanding membrane. The requisite greatly enhanced viscous flow of SiO2 underneath the Si layer is consistent with the dependence of the viscosity of SiO2 on shear stress.