  Within the covariant formulation of Light-Front Dynamics, in a scalar model
with the interaction Hamiltonian $H=-g\psi^{2}(x)\phi(x)$, we calculate
nonperturbatively the renormalized state vector of a scalar "nucleon" in a
truncated Fock space containing the $N$, $N\pi$ and $N\pi\pi$ sectors. The
model gives a simple example of non-perturbative renormalization which is
carried out numerically. Though the mass renormalization $\delta m^2$ diverges
logarithmically with the cutoff $L$, the Fock components of the "physical"
nucleon are stable when $L\to\infty$.
