Based on atomic force microscopy nanoindentation measurements of phage λ, we previously proposed a minimal model describing the effect of water hydrating DNA that strengthens viral capsids against external deformation at wild-type DNA packing density. Here, we report proof of this model by testing the prediction that DNA hydration forces can be dramatically decreased by addition of multivalent ions (Mg(2+) and Sp(4+)). These results are explained using a DNA hydration model without adjustable parameters. The model also predicts the stiffness of other DNA-filled capsids, which we confirm using bacteriophage ϕ29 and herpes simplex virus type 1 particles.