Modern systems are difficult to design because of a need to satisfy many different stakeholder concerns from a number of domains, which require a large amount of expert knowledge. Current systems engineering practices try to simplify the design process by providing practical approaches to manage the large amount of knowledge and information needed during the process. Although these methods make designing a system more practical, they do not support a structured decision making process, especially at early stages when designers are selecting the appropriate system architecture, and instead rely on designers using ad hoc frameworks that are often self-contradictory, i.e., they can lead to alternative orderings where alternative A is better than alternative B is better than alternative C which is then better than alternative A. In order to support a more rational design making process, designers need to explicitly model the architecture selection decision and related knowledge. Then computational tools can be applied to guide the decision making. As a first step toward this more comprehensive modeling approach, in this paper a language is presented for modeling system-level architecture decisions by capturing the relevant domain-specific knowledge. This language is based on the principles of decision-based design and decision theory, where decisions are made by picking the alternative, which results in the most preferred expected outcomes. Therefore, the language is designed to capture potential alternatives in a compact form, analysis knowledge used to predict the quality of a particular alternative, and evaluation criteria to differentiate between outcomes. This language is based on the Object Management Group’s System Modeling Language (SysML). Where possible, existing SysML constructs are used and when additional constructs are needed SysML’s profile mechanism is used to extend the language. The value of the language is demonstrated by using it to represent a simple architecture selection decision of the actuation subsystem of a hydraulic excavator. Since this language models the architecture decision in a form that is computer interpretable, model transformations can be used to generate relevant analyses that can guide the decision maker during the design process.