Depression and anxiety are among the most common mental health concerns for science and engineering (S&E) undergraduates in the United States (U.S.), and students perceive they would benefit from knowing a S&E instructor with depression or anxiety. However, it is unknown how prevalent depression and anxiety are among S&E instructors and whether instructors disclose their depression or anxiety to their undergraduates. These identities are unique because they are concealable stigmatized identities (CSIs), meaning they can be kept hidden and carry negative stereotypes. To address these gaps, we surveyed 2013 S&E faculty instructors across U.S. very high research activity doctoral-granting institutions. The survey assessed the extent to which they had and revealed depression or anxiety to undergraduates, why they chose to reveal or conceal their depression or anxiety, and the benefits of revealing depression or anxiety. These items were developed based on prior studies exploring why individuals conceal or reveal CSIs including mental health conditions. Of the university S&E instructors surveyed, 23.9% (n = 482) reported having depression and 32.8% (n = 661) reported having anxiety. Instructors who are women, white, Millennials, or LGBTQ+ are more likely to report depression or anxiety than their counterparts. Very few participants revealed their depression (5.4%) or anxiety (8.3%) to undergraduates. Instructors reported concealing their depression and anxiety because they do not typically disclose to others or because it is not relevant to course content. Instructors anticipated that undergraduates would benefit from disclosure because it would normalize struggling with mental health and provide an example of someone with depression and anxiety who is successful in S&E. Despite undergraduates reporting a need for role models in academic S&E who struggle with mental health and depression/anxiety being relatively common among U.S. S&E instructors, our study found that instructors rarely reveal these identities to their undergraduates.