System scenarios that derived from system design specification play an important role in the reliability engineering of component-based software systems. A great deal of research effort has been devoted to predict the reliability of a system at the design-time, only few papers address the challenges of modeling and calculation of scenarios reliability. This paper identifies various challenges related to scenario modeling at the early design stages based on software architecture specification. It discusses the truncation and modeling methods of scenarios, the related computation cost, and their effect on the approach scalability, which has been missed by most of the current approaches. The paper proposes a modeling and calculation approach that, pragmatically, models and divides scenarios by a scenario specification language and finite state machine. It utilizes mathematical formulas for the calculations. The proposed work can be used as part of the reliability prediction approach to model and calculate the reliability of scenarios. We demonstrate the applicability of our approach by modeling and calculating scenarios reliability of an automated railcar system.