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The technology of continuously welded rails (CWRs) is important in modern railway track structures. To measure rail stress, resistance strain gauges are preferred due to their good stability, sensitivity, and resistance to external interference. Based on the bi-directional strain method, we present a new method for measuring longitudinal rail stress using resistance strain gauges and develop a monitoring device for rail stress to realize long-term and multi-point measurement. Also relevant experimental verification and analysis are conducted. Results indicate that under various constraints the rail stress-strain values can be calculated just with the measured total longitudinal strain and total vertical strain. Considering the measurement error caused by sectional feature of sensors, we put forward a correction equation applicable to different stress conditions. Although the temperature values of the four full-bridge stress gauges can offset each other, the measurement error caused by rail flexural strain can also be eliminated to a certain extent at the same time, the nonuniform distribution of rail cross section temperature and unbalanced flexural strain still affect the measurement error. The experimental results also show that the developed rail-stress-monitoring sensor is suitable for measuring rail stress with reliable working performance.