Algorithms which can effectively detect epileptic seizures have the potential to improve current treatment methods for people who suffer from epilepsy. The current state-of-the-art methods use neural networks, which are able to learn directly from the electroencephalogram (EEG) data without feature extraction. However, neural networks have drawbacks—they are time and data intensive to train and require a high number of parameters for efficient classification. This thesis proposes a novel approach to the epileptic seizure detection problem using Support Tensor Machines (STMs). The final models learn directly from EEG data and use far fewer model parameters compared to a state-of-the-art model using a convolutional neural network. Three types of experiments have been conducted using different representations for the EEG data. The STMs used in the experiments are the Support Higher-Order Tensor Machine, Dual Structure-preserving Kernel (DuSK), and Tensor Train Multi-way Multi-level Kernel (TT-MMK). The results show that by using TT-MMK (with a tensorized data representation) for leave-one-seizure-out validation and DuSK (with the original data representation) for leave-one-patient-out validation, the models are able to rival a state-of-the-art epileptic seizure detector.