The size effect is the change of structural properties, especially nominal strength, due to scaling of geometrically similar structures. Due to the relatively large non-linear fracture process zone, the size effect on the nominal strength of a concrete structure is explained by non-linear fracture mechanics employing both an equivalent elastic crack model and a cohesive zone model (CZM) approach. The concept of equivalent elastic crack model provides the theoretical background for the size effect method (SEM) and the two-parameter fracture model (TPFM), which provide two size-independent fracture parameters. In addition, the CZM characterizes non-linear fracture process behavior through the bi-linear softening curve, which is determined by four experimental fracture parameters: tensile strength (ft), initial fracture energy (Gf ), total fracture energy (GF ) and critical crack tip opening displacement (CTODc). The location of the kink point in the bi-linear softening model has been estimated empirically in the literature. Thus a formal criterion to determine the kink point is proposed and discussed. The bi-linear softening curve in the CZM enables prediction of the load versus crack mouth opening displacement (CMOD) experimental curves as well as the size effect. Several examples and a sensitivity analysis are given to illustrate these points.