The Double Punch test, an indirect traction test, is simulated numerically considering two different models (the nonlocal Mazars damage model and an heuristic crack model with joint elements). The test was designed to measure indirectly the tensile strength of concrete, hence, through these two numerical models, we are able to assess the tensile strength numerically. Experimental results present scattering when assessing the tensile strength, therefore, other tests are needed to set all the material and geometrical parameters of the numerical models. Both models are validated for the Double Punch test.