This paper studies the relationship between the two parameter fracture model and the size effect model. An equivalency between two models is first established based on infinitely large size specimens. Based on this equivalency, relationships between material fracture parameters (KIcs, CTODc) and (Gf, cf) are derived. Using these relationships, values of (KIcs, CTODc) and (Gf, cf) can be predicted from each other. It is found that the relationship betweenCTODc andcf theoretically depends on both specimen geometry and initial crack length. However this dependency is numerically insignificant, except for tensile plate with a short center notch. The obtained results may explain why both the two parameter fracture model and the size effect model can reasonably predict fracture behavior of quasi-brittle materials.