Person reidentification usually refers to matching people in different camera views in nonoverlapping multicamera networks. Many existing methods learn a similarity measure by projecting the raw feature to a latent subspace to make the same target's distance smaller than different targets' distances. However, the same targets captured in different camera views should hold the same intrinsic attributes while different targets should hold different intrinsic attributes. Projecting all the data to the same subspace would cause loss of such an information and comparably poor discriminability. To address this problem, in this paper, a method based on elastic projections is proposed to learn a pairwise similarity measure for person reidentification. The proposed model learns two projections, positive projection and negative projection, which are both representative and discriminative. The representability refers to: for the same targets captured in two camera views, the positive projection can bridge the corresponding appearance variation and represent the intrinsic attributes of the same targets, while for the different targets captured in two camera views, the negative projection can explore and utilize the different attributes of different targets. The discriminability means that the intraclass distance should become smaller than its original distance after projection, while the interclass distance becomes larger on the contrary, which is the elastic property of the proposed model. In this case, prior information of the original data space is used to give guidance for the learning phase; more importantly, similar targets (but not the same) are effectively reduced by forcing the same targets to become more similar and different targets to become more distinct. The proposed model is evaluated on three benchmark data sets, including VIPeR, GRID, and CUHK, and achieves better performance than other methods.