Fatigue cracking caused by repeated heavy traffic loading is a critical distress in asphalt concrete pavements and is significantly affected by the selected binder. In recent years, the growing use of recycled asphalt materials has increased the need for the production of softer asphalt binder. Various modifiers/additives are marketed to adjust the grade and/or enhance the binder performance at high and low temperatures. The modifiers are expected to alter the rheological and chemical characteristics of binders and, therefore, their performance. In this study, the damage characteristics of modified and unmodified binders, at standard long-term and extended aging conditions, were tested using the linear amplitude sweep (LAS) test. Current datainterpretation methods for LAS measurements (including AASHTO TP 101-12, T 391-20, and recent literature) showed inconsistent results for modified binders. An alternative method to interpret LAS results was developed in this study. The method considers the data until peak shear-stress is reached because complex stress states and failure patterns are observed in the specimens after that point. The proposed parameter (D|G*|peak t) quantifies the reduction in complex shear modulus measured at the peak shear-stress. The parameter successfully captures the effect of aging and modification of binders.