Machine learning has been widely adopted in diverse science and engineering domains, aided by reusable libraries and quick development patterns. The TensorFlow library is probably the best-known representative of this trend and most users employ the Python API to its powerful back-end. TensorFlow programs are susceptible to several systematic errors, especially in the dynamic typing setting of Python. We present a static analysis that tracks the shapes of tensors across Python library calls and warns of several possible mismatches. The key technical aspects are a close modeling of library semantics with respect to tensor shape, and an identification of violations and error-prone patterns. Our analysis is powerful enough to statically detect (with 100% precision) 11 of the 14 shape-related TensorFlow bugs in the recent Zhang et al. empirical study—an independent slice of real-world bugs that also includes semantic violations not statically detectable.