Abstract In the present study, a new algorithm, in which the first five terms of stress field near the crack-tip were included in the analysis, has been proposed for capturing size effect phenomena in self-compacting normal weight concrete (SCC) and self-compacting lightweight concrete (SCLC). In this algorithm, the length of fracture process zone (FPZ) was determined analytically by assuming that the onset of fracture occurs when the normal-to-crack component of stress-field reaches the tensile strength of material. To evaluate the method, 156 notched beam specimen of different sizes were analyzed and the results of the proposed algorithm have been compared with those of experiments. Results indicate that the method is capable of capturing size effects in SCC and SCLC as well as representing a new insight in modeling of fracture behavior of SCC and SCLC. Moreover, the method is able to predict the load carrying capacity of the specimens with good precisions.