In this work we explore Unsupervised Domain Adaptation (UDA) of pretrained language models for downstream tasks. We introduce UDALM, a fine-tuning procedure, using a mixed classification and Masked Language Model loss, that can adapt to the target domain distribution in a robust and sample efficient manner. Our experiments show that performance of models trained with the mixed loss scales with the amount of available target data and the mixed loss can be effectively used as a stopping criterion during UDA training. Furthermore, we discuss the relationship between A-distance and the target error and explore some limitations of the Domain Adversarial Training approach. Our method is evaluated on twelve domain pairs of the Amazon Reviews Sentiment dataset, yielding 91.74% accuracy, which is an 1.11% absolute improvement over the state-of-the-art.