Recent studies have shown that today's college students more than ever are struggling with mental health and alcohol problems. While poor satisfaction with life and mental health problems have been linked to higher alcohol consumption, there is still a lack of studies examining in detail the shape and nature of the relationship between mental health and alcohol consumption. To investigate the associations between satisfaction with life, mental health problems and potential alcohol-related problems among Norwegian university students. The shape of the associations was also examined. Data were drawn from a 2018 national survey of students in higher education in Norway (the SHoT-study). Associations between satisfaction with life, mental health problems and potential alcohol-related problems (AUDIT; risky and harmful alcohol use) were investigated using logistic regression. Both crude models and models adjusted for age, gender and marital status were conducted. To investigate the shape of the associations, logistic regression with quadric and cubic terms was tested. Decreased satisfaction with life and increased mental health problems were associated with potential alcohol-related problems. For satisfaction with life, a curvilinear association with risky alcohol use and a linear association with harmful alcohol use was identified. For mental health problems, curvilinear associations were found for both risky and harmful alcohol use. Many students report potential alcohol-related problems. Students with harmful alcohol use seem to be more at risk of reduced satisfaction with life and increased mental health problems than students with risky alcohol use. Educational institutions may be an ideal setting for raising awareness of mental health issues and responsible alcohol consumption among students. The present study contributes with important information about the shape of the associations between satisfaction with life, mental health problems and potential alcohol-related problems in the student population.