A thermo-mechanical simulation of the wire + arc additive manufacturing (WAAM) process is presented in this work. The simulation consists in the deposition of 5 successive layers of 316 L stainless steel on a 316 L base plate. The thermo-mechanical analysis is solved in two dimensions under plane stress assumption. Nonetheless, the metal addition is taking into account in this numerical analysis. An increment of material is added at each time step. This numerical approach allows reducing the computational time. The temperature and residual stress fields are computed at each time step. Two patterns of deposition strategy are also investigated. It is shown that the longitudinal stress varies mainly along the vertical axis. A sample with 5 overlaid layers has been scanned with neutron diffraction technique in order to measure the final residual stresses. Both numerical and measured residual stresses are in good agreement. The Aster finite element software is employed for the numerical analysis.