Many fracture mechanics models have been proposed in recent years to account for the non-linear behavior of concrete around the crack tip region. These well-known models are the Fictitious Crack Model (FCM) by Ilillcrborg, the Crack Band Model (CBM) by Bazant, and the Two-Parameter Fracture Model (TPFM) by Jenq and Shah, etc. To model the fracture process zone or microcrackcd zone, these models often assumed the linear or bilinear stress-displacement relationship to simplify the analysis since actual relationships were not available due to difficulties in conducting direct tension test. To avoid tedious numerical computation and the need of.stress-displacement relationship, TPFM was proposed based on the simple LEFM concept. The model was quite accurate when applied to notched beam test. All these models presented some degree of satisfaction when comparing with some experimental data. Since more direct tension tests with complete post-peak stress-displacement relationships have been successfully conducted in recent years, the need of assuming the stress-displacement relationship or using the indirect notched beam test is no longer necessary. An evaluation of the FCM using the observed stress-displacement relationships versus the assumed one seems to be an interesting task to verify the validity of the model. For TPFM, the proposed two unique fracture parameters (KSIcand CTODcc) should be verified for specimen size-independence. A scries of experiments were conducted on two types of test specimen (notched beam and compact tension) with different geometries. The results indicate that KSIcand CTODcrecommended in TPFM seem to be unique only for the notched beam specimen. The same two parameters were found to be 10 fold larger for the compact tension specimen. For FCM, the predicted load-CMOD and load-deflection curves using the observed stress-displacement relationship arc in better agreement with experimental data than those determined from the assumed linear relationship. Although theoretically both predicted load-CMOD and load-deflection curves should have the same order of accuracy, in this study, they were found to be substantially different.