Banks and other financial institutions are to a certain extent obligated to ensure that their services are not utilized for any type of financial crime. This thesis investigates the possibility of analyzing bank customers' transactional behaviour with machine learning to detect if they are involved in financial crime. The purpose of this is to see if a new approach to processing and analyzing transaction data could make financial crime detection more accurate and efficient. Transactions of a customer over a time period are processed to form multivariate time series. These time series are then used as input to different machine learning models for time series classification. The best method involves a transform called Random Convolutional Kernel Transform that extracts features from the time series. These features are then used as input to a logistic regression model that generates probabilities of the different class labels. This method achieves a ROC AUC-score of 0.856 when classifying customers as being involved in financial crime or not. The results indicate that the time series models detect patterns in transaction data that connect customers to financial crime which previously investigated methods have not been able to find.