We investigate the ground-state properties of the Anderson single impurity model (finite Coulomb impurityrepulsion) with the Coupled Cluster Method.We consider different CCM reference states and approximation schemesand make comparison with exact Green's function results for the non-interacting model and with Brillouin-Wignerperturbation theory for the full interacting model.Our results show that coupled cluster techniques are well suited toquantum impurity problems.