Hybrid software processes are defined as a combination of practices from traditional and agile methodologies. Most software development companies currently apply this kind of process; however, the appropriate combination of practices is not often clear. To address this issue, we have proposed DynaTail in a previous study, i.e., a method for tailoring a software process and its practices to a particular context to improve a certain characteristic. In this work, we use an MDE approach to formalize all the artifacts involved in DynaTail: processes, context, practices influencing goals, and tailoring transformations. This model-based formalization lays the base for building supporting tools. We illustrate all models with a running example from a Chilean medium-size software development company.