Recurrent Neural Networks (RNNs) are one of the most successful neural network architectures that deal with temporal sequences, e.g., speech and text recognition. Recently, RNNs have been shown to be useful in cognitive neuroscience as a model of decision-making. RNNs can be trained to solve the same behavioral tasks performed by humans and other animals in decision-making experiments, allowing for a direct comparison between networks and experimental subjects. Analysis of RNNs is expected to be a simpler problem than the analysis of neural activity. However, in practice, reasoning about an RNN's behaviour is a challenging problem. In this work, we take an approach based on formal verification for the analysis of RNNs. We make two main contributions. First, we consider the cognitive domain and formally define a set of useful properties to analyse for a popular experimental task. Second, we employ and adapt wellknown verification techniques for reachability analysis to our focus domain, i.e., polytope propagation, invariant detection, and counter-example-guided abstraction refinement. Our experiments show that our techniques can effectively solve classes of benchmark problems that are challenging for state-of-the-art verification tools.