Potentially idiomatic expressions (PIEs) are ambiguous between non-compositional idiomatic interpretations and transparent literal interpretations. For example, hit the road'' can have an idiomatic meaning corresponding to start a journey' or have a literal interpretation. In this paper we propose a supervised model based on contextualized embeddings for predicting whether usages of PIEs are idiomatic or literal. We consider monolingual experiments for English and Russian, and show that the proposed model outperforms previous approaches, including in the case that the model is tested on instances of PIE types that were not observed during training. We then consider cross-lingual experiments in which the model is trained on PIE instances in one language, English or Russian, and tested on the other language. We find that the model outperforms baselines in this setting. These findings suggest that contextualized embeddings are able to learn representations that encode knowledge of idiomaticity that is not restricted to specific expressions, nor to a specific language.