Negative and uncertain medical findings are frequent in radiology reports, but discriminating them from positive findings remains challenging for information extraction. Here, we propose a new algorithm, NegBio, to detect negative and uncertain findings in radiology reports. Unlike previous rule-based methods, NegBio utilizes patterns on universal dependencies to identify the scope of triggers that are indicative of negation or uncertainty. We evaluated NegBio on four datasets, including two public benchmarking corpora of radiology reports, a new radiology corpus that we annotated for this work, and a public corpus of general clinical texts. Evaluation on these datasets demonstrates that NegBio is highly accurate for detecting negative and uncertain findings and compares favorably to a widely-used state-of-the-art system NegEx (an average of 9.5% improvement in precision and 5.1% in F1-score).