This study investigates some technical issues related to the use of cohesive zone models (CZMs) in modeling the fracture of materials with negligible plasticity outside the fracture process zone. These issues include: (1) why cohesive laws of different shapes can produce similar fracture predictions, (2) under what conditions CZM predictions have a high degree of agreement with linear elastic fracture mechanics (LEFM) analysis results, (3) when the shape of cohesive laws becomes important in the fracture predictions, and (4) why the opening profile along the cohesive zone length (CZL) needs to be accurately predicted. Two cohesive models were used in this study to address these technical issues. They are the linear softening cohesive model and the Dugdale perfectly plastic cohesive model. Each cohesive model uses five cohesive laws of different maximum tractions. All cohesive laws have the same cohesive work rate (CWR) defined by the area under the traction–separation curve. The effects of the maximum traction on the cohesive zone length and the critical remote applied stress are investigated for both models. The following conclusions from this study may provide some guidelines for the prediction of fracture using CZM. For a CZM to predict a fracture load similar to that obtained by an LEFM analysis, the cohesive zone length needs to be much smaller than the crack length, which reflects the small-scale yielding condition requirement for LEFM analysis to be valid. For large-scale cohesive zone cases, the predicted critical remote applied stresses depend on the shape of the cohesive models used and can significantly deviate from LEFM results. Furthermore, this study also reveals the importance of accurately predicting the cohesive zone profile for determining the critical remote applied load.