In sentiment analysis of product reviews, both user and product information are proven to be useful. Current works handle user profile and product information in a unified model which may not be able to learn salient features of users and products effectively. In this work, we propose a dual user and product memory network (DUPMN) model to learn user profiles and product information for reviews classification using separate memory networks. Then, the two representations are used jointly for sentiment analysis. The use of separate models aims to capture user profiles and product information more effectively. Comparing with state-of-the-art unified prediction models, evaluations on three benchmark datasets (IMDB, Yelp13, and Yelp14) show that our dual learning model gives performance gain of 0.6%, 1.2%, and 0.9%, respectively. The improvements are also deemed very significant measured by p-values.