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• The detection and evaluation of reinforcement elastic stress in RC beams were studied. • The magnetic signal gradient was quantitatively modeled and verified by experiments. • A method based on Bayesian theory was developed to estimate the elastic stress. • This method can be reliably applied for rapid and economic stress detection in RC beams. This study developed a method for detection and quantitative evaluation of the elastic stress of the reinforcement in reinforced concrete (RC) beams. By combining the minimum energy and magnetic dipole theories, a quantitative model of the magnetic signal gradient and magnetization angle was established. The spatial distribution of the magnetic signals and variation of the average gradient with stress in the pure bending section of the RC beams were obtained through four-point bending experiments. The results show that the law of the average gradient with the stress is consistent with that predicted by the theoretical model. Based on the Bayesian theory, a method to evaluate the elastic stress was established, which can be applied for grading the elastic stress of the reinforcement within a certain range of accuracy. [ABSTRACT FROM AUTHOR]