In recent years, Transformers have become the de-facto architecture for sequence modeling on text and multi-dimensional data, such as images and video. However, the use of self-attention layers in a Transformer incurs prohibitive compute and memory complexity that scales quadratically w.r.t. the sequence length. A recent architecture, Mamba, based on state space models has been shown to achieve comparable performance for modeling text sequences, while scaling linearly with the sequence length. In this work, we present Mamba-ND, a generalized design extending the Mamba architecture to arbitrary multi-dimensional data. Our design alternatively unravels the input data across different dimensions following row-major orderings. We provide a systematic comparison of Mamba-ND with several other alternatives, based on prior multi-dimensional extensions such as Bi-directional LSTMs and S4ND (Fig. 1). Empirically, we show that Mamba-ND demonstrates performance competitive with the state-of-the-art on various multi-dimensional benchmarks, including ImageNet-1K classification, HMDB-51 and UCF-101 action recognition, ERA5 weather forecasting and BTCV 3D segmentation. Code is available at https://github.com/jacklishufan/Mamba-ND