A well-defined software process is critical for success in software projects. Software process tailoring refers to the activity of tuning a standardized process to meet the needs of a specific project. We conducted two case studies that address the research question: How is a software process tailored to suit its context? This study identifies process tailoring as a key mechanism to address the challenges faced by a project and develops a model that describes how a process is tailored to resolve these challenges. The model identifies a set of environmental factors, challenges, project goals, process tailoring strategies, and their influences on each other. Specifically, the findings demonstrate the duality of the software process, showing how the project context (i.e., project goals, environmental factors, and challenges) and tailoring decisions dynamically interact with each other and construct the context in which the project is developed and the process is tailored.