Understanding tables is an important aspect of natural language understanding. Existing models for table understanding require linearization of table contents in certain levels, where row or column orders are encoded as unwanted biases. Such spurious biases make the model vulnerable to row and column order perturbations. Also, prior work did not explicitly and thoroughly model structural biases, hindering the table-text modeling ability. In this work, we propose a robust table-text encoding architecture TableFormer, where tabular structural biases are incorporated completely through learnable attention biases. TableFormer is invariant to row and column orders, and could understand tables better due to its tabular inductive biases. Experiments showed that TableFormer outperforms strong baselines in all settings on SQA, WTQ and TabFact table reasoning datasets, and achieves state-of-the-art performance on SQA, especially when facing answer-invariant row and column perturbations (6% improvement over the best baseline), because previous SOTA models' performance drops by 4% - 6% when facing such perturbations while TableFormer is not affected.