The competency-based education model has been one of the paths taken by higher education institutions concerned with offering programs relevant to the market and societal needs. However, adapting teaching to a competency-based education model can bring many challenges, such as assessing and monitoring competencies. Indeed, few studies address how to structure and implement a comprehensive competency-based education model and systematically assess and monitor competence development. This article proposes a method for evaluating the development of curricular competencies of Industrial Engineering undergraduate students at the Federal University of Rio Grande do Sul in Southern Brazil. The method uses assessment rubrics as a tool for faculty to assess student competence development throughout the entire program. More specifically, we propose rubrics to assess competencies at three stages: initial (first semesters of the program), intermediate (approximately halfway through the program), and final (final semesters) in order to track their development throughout the program. The developed method follows four steps: i) selection of the courses for the competence assessment; ii) development of the assessment rubrics; iii) definition of methods and tools for applying rubrics; and iv) definition of how competence assessment rubrics would be organized and communicated. The assessment rubric developed is a table-like structure composed of four parts. The first has the three elements of competencies (knowledge, skills and attitudes). The second has the expected learning outcome for each one of the three elements. The third has the descriptors for each of the four performance levels (beginner, under development, satisfactory, and advanced) per learning outcome. The fourth and last one shows the courses where each learning outcome will be assessed. The method was tested in an Industrial Engineering undergraduate program at the Federal University of Rio Grande do Sul in Brazil. Regarding the assessment results, the method proposes that faculty members must provide feedback to students and use these results to promote improvement in the development of competencies throughout the course. This method allows the undergraduate program to monitor how students developed each competence at different performance levels throughout the courses. Based on the results, we expect to encourage the method's use to monitor the development of university students' competencies.