High-order tensor data are prevalent in real-world applications,and multiway clustering is one of the most important techniques for exploratory data mining and compression of multiway data.However,existing multiway clustering is based on the K-means procedure and is incapable of addressing the issue of crossed membership degrees.To overcome this limitation,we propose a flexible multiway clustering model called approximately orthogonal nonnegative Tucker decomposition (AONTD).The new model provides extra flexibility to handle crossed memberships while fully exploiting the multilinear property of tensor data.The accelerated proximal gradient method and the low-rank compression tricks are adopted to optimize the cost function.The experimental results on both synthetic data and real-world cases illustrate that the proposed AONTD model outperforms the benchmark clustering methods by significantly improving the interpretability and robustness.