Objective: The detection of epileptic seizures from scalp electroencephalogram (EEG) signals can facilitate early diagnosis and treatment. Previous studies suggested that the Gaussianity of EEG distributions changes depending on the presence or absence of seizures; however, no general EEG signal models can explain such changes in distributions within a unified scheme. Methods: This article describes the formulation of a stochastic EEG model based on a multivariate scale mixture distribution that can represent changes in non-Gaussianity caused by stochastic fluctuations in EEG. In addition, we propose an EEG analysis method by combining the model with a filter bank and introduce a feature representing the non-Gaussianity latent in each EEG frequency band. Results: We applied the proposed method to multichannel EEG data from twenty patients with focal epilepsy. The results showed a significant increase in the proposed feature during epileptic seizures, particularly in the high-frequency band. The feature calculated in the high-frequency band allowed highly accurate classification of seizure and non-seizure segments [area under the receiver operating characteristic curve (AUC) = 0.881] using only a simple threshold. Conclusion: This article proposed a multivariate scale mixture distribution-based stochastic EEG model capable of representing non-Gaussianity associated with epileptic seizures. Experiments using simulated and real EEG data demonstrated the validity of the model and its applicability to epileptic seizure detection. Significance: The stochastic fluctuations of EEG quantified by the proposed model can help detect epileptic seizures with high accuracy.