Deep learning models suffer from a phenomenon called adversarial attacks: we can apply minor changes to the model input to fool a classifier for a particular example. The literature mostly considers adversarial attacks on models with images and other structured inputs. However, the adversarial attacks for categorical sequences can also be harmful. Successful attacks for inputs in the form of categorical sequences should address the following challenges: (1) non-differentiability of the target function, (2) constraints on transformations of initial sequences, and (3) diversity of possible problems. We handle these challenges using two black-box adversarial attacks. The first approach adopts a Monte-Carlo method and allows usage in any scenario, the second approach uses a continuous relaxation of models and target metrics, and thus allows usage of state-of-the-art methods for adversarial attacks with little additional effort. Results for money transactions, medical fraud, and NLP datasets suggest that proposed methods generate reasonable adversarial sequences that are close to original ones but fool machine learning models.