We demonstrate that the polaron theory from solid state physics can serve as an interesting analogue model for non-perturbative QCD, at least in the description of nucleons and related low-energy physics of strong interactions. By drawing explicit analogies between polaron physics, arising for an electron moving in an ionic crystal, and physics of pion-nucleon interactions, certain rules for the “polaron/QCD correspondence” are proposed. In polaron theory, the effective fermion mass as a function of the coupling constant is known both in the weak and strong coupling limits. The conjectured “polaron/QCD correspondence” translates these results into strong interactions. It is then shown how application of these rules leads to unexpectedly good quantitative predictions for the nucleon mass and pion-nucleon sigma term. The polaron approach also predicts that the quark degrees of freedom in the form of the constituent quark account for onethird of the nucleon mass, consistent with lattice predictions. We discuss possible physical reasons underlying the observed quantitative similarity between polaron physics and non-perturbative QCD.