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Using atomistic calculations with a Finnis-Sinclair type potential and molecular statics and dynamics methods, we performed a series of deformation tests on nanocrystallised tungsten samples presenting various microstructures; we calculated the elastic constants of polycrystalline tungsten for average grain diameters ranging from 2.7 to 6.7 nm. The results show that both Young’s and the shear moduli decrease by over 60% as the average grain diameter decreases below 3 nm. This diminution appears to be highly correlated to the grain boundary volume fraction. The results are compared to conclusions from other authors.