Under-reporting and delayed reporting of rape crime are severe issues that can complicate the prosecution of perpetrators and prevent rape survivors from receiving needed support. Building on a massive database of publicly available criminal reports from two US cities, we develop a machine learning framework to predict delayed reporting of rape to help tackle this issue. Motivated by large and unexplained spatial variation in reporting delays, we build predictive models to analyse spatial, temporal and socio-economic factors that might explain this variation. Our findings suggest that we can explain a substantial proportion of the variation in rape reporting delays using only openly available data. The insights from this study can be used to motivate targeted, data-driven policies to assist vulnerable communities. For example, we find that younger rape survivors and crimes committed during holiday seasons exhibit longer delays. Our insights can thus help organizations focused on supporting survivors of sexual violence to provide their services at the right place and time. Due to the non-confidential nature of the data used in our models, even community organizations lacking access to sensitive police data can use these findings to optimize their operations.