In this work we explore the applicability of the recently proposed CNN architecture, called Bilinear CNN, and its new modification that we call multi-region Bilinear CNN to the person re-identification problem. Originally, Bilinear CNNs were introduced for fine-grained classification and proved to be both simple and high-performing architectures. Bilinear CNN allows to build an orderless descriptor for an image using outer product of features outputted from two separate feature extractors. Based on this approach, Multiregion Bilinear CNN, apply bilinear pooling over multiple regions for extracting rich and useful descriptors that retain some spatial information. We show than when embedded into a standard "siamese" type learning, bilinear CNNs and in particular their multi-region variants can improve re-identification performance compared to standard CNNs and achieve state-of-the-art accuracy on the largest person re-identification datasets available at the moment, namely CUHK03 and Market-1501.