Crafting adversarial examples has become an important technique to evaluate the robustness of deep neural networks (DNNs). However, most existing works focus on attacking the image classification problem since its input space is continuous and output space is finite. In this paper, we study the much more challenging problem of crafting adversarial examples for sequence-to-sequence (seq2seq) models, whose inputs are discrete text strings and outputs have an almost infinite number of possibilities. To address the challenges caused by the discrete input space, we propose a projected gradient method combined with group lasso and gradient regularization. To handle the almost infinite output space, we design some novel loss functions to conduct non-overlapping attack and targeted keyword attack. We apply our algorithm to machine translation and text summarization tasks, and verify the effectiveness of the proposed algorithm: by changing less than 3 words, we can make seq2seq model to produce desired outputs with high success rates. We also use an external sentiment classifier to verify the property of preserving semantic meanings for our generated adversarial examples. On the other hand, we recognize that, compared with the well-evaluated CNN-based classifiers, seq2seq models are intrinsically more robust to adversarial attacks.