Automatic identification of clinical trials for which a patient is eligible is complicated by the fact that trial eligibility is stated in natural language. A potential solution to this problem is to employ text classification methods for common types of eligibility criteria. In this study, we focus on seven common exclusion criteria in cancer trials: prior malignancy, human immunodeficiency virus, hepatitis B, hepatitis C, psychiatric illness, drug/substance abuse, and autoimmune illness. Our dataset consists of 764 phase III cancer trials with these exclusions annotated at the trial level. We experiment with common transformer models as well as a new pre-trained clinical trial BERT model. Our results demonstrate the feasibility of automatically classifying common exclusion criteria. Additionally, we demonstrate the value of a pre-trained language model specifically for clinical trials, which yields the highest average performance across all criteria.