In this talk we address the solution of quasilinear elliptic problems of monotone type by using the Mimetic Finite Difference (MFD) method. Under a suitable approximation assumption, we prove that the MFD approximate solution converges to the exact solution in a mesh-dependent energy norm. The resulting nonlinear discrete problem is then solved iteratively via linearization by applying the Kacanov method, which is shown to be convergent. Several numerical experiments confirm the theoretical analysis. This is a joint work with P.F. Antonietti (PoliMi) and N. Bigoni (PoliMi).