Undergraduate research experiences are a "high impact" educational practice that confer benefits to students. However, little attention has been paid to understanding faculty motivation to mentor undergraduate students through research training programs, even as the number of programs has grown, requiring increasing numbers of faculty mentors. To address this, we introduce a conceptual model for understanding faculty motivation to mentor and test it by using empirical data to identify factors that enable and constrain faculty engagement in an undergraduate research program. Using cross-sectional survey data collected in 2013, we employed generalized linear modeling to analyze data from 536 faculty across 13 research institutions to examine how expected costs/benefits, dispositional factors, situational factors, previous experience, and demographic factors predicted faculty motivation to mentor. Results show that faculty who placed greater value on the opportunity to increase diversity in the academy through mentorship of underrepresented minorities were more likely to be interested in serving as mentors. Faculty who agreed more strongly that mentoring undergraduate students was time consuming and their institution's reward structures were at odds with mentoring, or who had more constrained access to undergraduate students were less likely to be interested in serving as mentors. Mid-career faculty were more likely than late-career faculty to be interested in serving as mentors. Findings have implications for improving undergraduate research experiences, since the success of training programs hinges on engaging highly motivated faculty members as mentors.