The unstructured and dynamic nature of construction projects and the on-site work complexities have been inevitably leading to claims. These evolve according to a staged mechanism set forth in the adopted conditions of contracts. More specifically, claims might progress expeditiously or drag depending on the nature of the applied mechanism and the behavior and interaction among contractual parties. As such, this complex problem of claim progression, which entails a lot of parameters and variables, is addressed in detail in this paper by resorting to three simulation techniques namely: (1) Discrete-Event Simulation (DES), (2) Agent-Based Modeling (ABM), and (3) System Dynamics (SD). The purpose behind this study is two-fold: (1) capturing and visualizing, through three different simulation models, the dynamic and interaction among the different entities as claims are progressing and defining the weak links hindering the efficiency improvement of such a process, and (2) comparing DES, ABM, and SD simulation approaches, using choose-by-advantage technique, and evaluating the advantages and drawbacks of each when studying the progression of claims. Results of all approaches are presented and analyzed followed by a discussion of the effectiveness of each simulation technique and the potential applicability of a hybrid approach in modeling the progression of claims.