Residual stresses have been characterized in four Wire Arc Additive Manufacturing specimens with neutron diffraction technique. Firstly, two methods are investigated for obtaining the reference diffracted angle θ0 that is required for the computation of micro-strains and, thus, the stresses. θ0 was obtained using two approaches. The first one required a strain-free specimen in order to get directly the reference diffracted angles θ0 in three directions. The second one is based on the plane stress assumption to get θ0 indirectly by imposing that the normal stress was equal to zero. Both methods led to similar residual stress profiles for the 1-layer specimen what validated this approach for all specimens that did not have a strain-free specimen available. The second part of this work focused on the effect of addition of a new layer on residual stresses. The measurements showed that the longitudinal stress was tensile in the Heat Affected Zone (HAZ) and Fusion Zone (FZ) with a maximum value located at the parent material - layers interface where the thermal loadings were applied. A decrease of this maximum value from 257 MPa to 199 MPa appeared after deposition of a new layer which is due to some stress relaxation effect. Inside the parent material, a large zone presents compressive longitudinal stress up to -170 MPa. The bottom part of the parent material is under tensile stress likely due to its upward bending following the thermal contraction of the deposited layers during cooling to ambient temperature.