Abstract: Using the concept of a permissible damage scale, the strain in front of crack tips in concrete were obtained as a third-order series based on the stress expressed by a William series, and the analytical solution of the permissible damage scale was derived based on the stress relaxation method. Taking a concrete beam specimen of finite size in three-point bending as an example, the theoretical values on the permissible damage scale were compared to the corresponding experimental values, and the influence of the series order on the value of permissible damage scale was analyzed. The results show that the theoretical values of permissible damage scale agree well with the experimental values. The values of permissible damage scale determined by the stress series expanded to T-stress terms are greater than the corresponding values by the singular term or expanded to the higher order terms as well as being much closer to the experimental values.