Process skills such as critical thinking and information processing are commonly stated outcomes for STEM undergraduate degree programs, but instructors often do not explicitly assess these skills in their courses. Students are more likely to develop these crucial skills if there is constructive alignment between an instructor's intended learning outcomes, the tasks that the instructor and students perform, and the assessment tools that the instructor uses. Rubrics for each process skill can enhance this alignment by creating a shared understanding of process skills between instructors and students. Rubrics can also enable instructors to reflect on their teaching practices with regard to developing their students' process skills and facilitating feedback to students to identify areas for improvement. Here, we provide rubrics that can be used to assess critical thinking and information processing in STEM undergraduate classrooms and to provide students with formative feedback. As part of the Enhancing Learning by Improving Process Skills in STEM (ELIPSS) Project, rubrics were developed to assess these two skills in STEM undergraduate students' written work. The rubrics were implemented in multiple STEM disciplines, class sizes, course levels, and institution types to ensure they were practical for everyday classroom use. Instructors reported via surveys that the rubrics supported assessment of students' written work in multiple STEM learning environments. Graduate teaching assistants also indicated that they could effectively use the rubrics to assess student work and that the rubrics clarified the instructor's expectations for how they should assess students. Students reported that they understood the content of the rubrics and could use the feedback provided by the rubric to change their future performance.