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A novel deep architecture, the sparse deep tensor extreme learning machine (SDT-ELM), is presented as a tool for pattern classification. In extending the original ELM, the proposed SDT-ELM gains the theoretical advantage of effectively reducing the number of hidden-layer parameters by using tensor operations, and using a weight tensor to incorporate higher-order statistics of the hidden feature. In addition, the SDT-ELM gains the implementation advantage of enabling the random hidden nodes to be added block by block, with all blocks having the same hidden layer configuration. Moreover, an SDT-ELM without randomness can also achieve better learning accuracy. Extensive experiments with three widely used classification datasets demonstrate that the proposed algorithm achieves better generalization performance.