Teaching and learning in the 21st century should equip students with critical and creative thinking skills to be ready to live and contribute productively to society. One suitable learning approach is integrating STEAM education and computational thinking--the STEAM-CT approach. The present study aims to describe students' critical and creative thinking skills in STEAM-CT integrative learning. The descriptive qualitative method was employed in this study. The current study included 26 eighth-grade students from a private middle school in Yogyakarta, Indonesia. According to the analysis, the students demonstrated critical and creative thinking skills during the integrative STEAM-CT learning process, particularly in planning problem solving, flexibility in providing problem solutions, and the aesthetics of their product designs. However, students must still be encouraged to conduct in-depth evaluations and use the results for improvement. For recommendation, to promote students' critical and creative thinking skills, feedback practices could be embedded in teaching and learning.