Traditional models of pull-apart basins usually develop along two strike-slip faults. However, there is an important variant that does not fit with the traditional pull-apart basins. This study presents this type of pull-apart basin called composite pull-apart basin formed in a strike-slip system consisting of multiple master fault segments. A set of two-dimensional discontinuum based, scaled, elastic models in upper crust are built to provide insights on composite pull-apart basin evolution. Three representative fault segment interaction geometries are modeled, showing underlapping, neutral, and overlapping releasing steps. They produce similar composite pull-apart basins consisting of two or three en echelon rhomboidal subbasins as offset increases. However, a change of initial fault geometry from underlapping to neutral and overlapping causes the fracture pattern to be more diffuse. The underlapping model produces a composite pull-apart basin with a throughgoing fault evolving from cross-basin faults in the subbasins whereas composite pull-apart basins produced in neutral and overlapping systems have no cross-basin faults and throughgoing faults. Modeling results show that local extension in underlapping systems with both pure strike-slip and 5 degrees transtension is accommodated through development of R-shears, small subbasins, cross-basin faults obliquely cutting the subbasins, and throughgoing fault. The morphology and structural evolution of composite pull-apart basins are determined by factors including pre-existing master strike-slip fault geometries (underlapping, neutral, or overlapping), fault kinematics (pure strike-slip, transtension, or transpression), and strike-slip displacements corresponding to evolution stages. The composite pull-apart basin geometries and fracture patterns of our numerical models fit well with natural examples such as the Gulf of Aqaba and the northern part of the Marmara Sea.