Background: Computation and computational thinking are of great interest to both engineering research and teaching communities. Effective learning environments are needed to incorporate computational thinking within the engineering disciplines. Design-based research is uniquely positioned to address this need for designing effective learning environments. Purpose: This design-based research study characterizes the different ways in which students used computational thinking when building computational models. The design of the model-building activities was grounded in productive failure and model-eliciting activities. Design: The design-based research study implemented the computational modeling activities within an engineering capstone course. The research question was: "What types of computational thinking outcomes emerge when engineering students build computational models?" Thematic analysis was applied to individual student artifacts to identify key computational thinking outcomes that were elicited as a result of the intervention. Results: Throughout the building of the model, students demonstrated the use of computational thinking outcomes, mainly abstraction, algorithmic thinking, evaluation, generalization, and decomposition. However, the diversity and density of use for each outcome were different and unique. Conclusions: This study shows how building computational models, when guided by current educational theories, can allow for students to practice the use of computational thinking and for educators to incorporate these key practices into their engineering classrooms.