In order to investigate the effect of flange on the shear capacity of reinforced concrete (RC) beams without stirrups, this study took into the contribution of compression zone, dowel action, and aggregate interlock in tension zone, and proposed a shear capacity calculation formula for RC beams without stirrups based on the crack sliding model. To verify the accuracy of the formula, the study used the formula and major design codes to calculate the collected experimental data of 444 rectangular beams and 172 T-shaped beams, and the results were compared with the results of major design codes. Five commonly used machine learning algorithms were used for regression analysis on the collected dataset, to verify the fit of each algorithm with a small dataset to analysis on the collected data, and the fitness of each algorithm was validated with a small dataset. The results show that: the shear capacity calculation method proposed by the codes of each country is in good agreement with the test results; compared to the calculation of the codes, the addressed calculation method herein is more accurate and can effectively account for the contribution of the T-beam flange to the shear capacity; the five machine learning models selected in this paper exhibit a desirable accuracy on the test set, and the results show the same trend as calculations; it also demonstrates the applicability of the machine learning models in the calculation of the shear capacity for reinforced concrete beams.