  We consider the classical limit of the Nelson model, a system of stable
nucleons interacting with a meson field. We prove convergence of the quantum
dynamics towards the evolution of the coupled Klein-Gordon-Schr\"odinger
equation. Also, we show that the ground state energy level of $N$ nucleons,
when $N$ is large and the meson field approaches its classical value, is given
by the infimum of the classical energy functional at a fixed density of
particles. Our study relies on a recently elaborated approach for mean field
theory and uses Wigner measures.
