Apart from the high accuracy of machine learning models, what interests many researchers and practitioners in real-life problems (e.g., fraud detection, credit scoring) is finding hidden patterns in the data. In this concern, intrinsically interpretable models are often preferred to complex ones, which are in most cases black-box models. Also, glass-box models such as linear regression or shallow decision trees are used in some high-risk fields to handle tabular data, even if performance must be sacrificed. In this paper, we propose TabSRAs, a new class of accurate tabular learning models with inherent intelligibility. TabSRAs are based on SRA (Self-Reinforcement Attention), a new attention mechanism that helps to learn an intelligible representation of the raw input data through element-wise vector multiplication. The learned representation is aggregated by a highly transparent function (e.g., linear) that produces the final output. Our results on synthetic and real-world data show that TabSRAs perform comparably to state-of-the-art models, while remaining self-explainable. Source code is available at https://github.com/anselmeamekoe/TabSRA .