In order to study the stress intensification effect of pipe elbow in the secondary stress check, the U-shaped pipeline commonly used in engineering was taken as the research object. The experiment platform for analysing pipe elbow stress was established, and the maximum stress with the displacement load was measured and compared with the results of the finite element analysis results and ASME B31.3 Code. On this basis, a correction formula calculating the Stress Intensification Factor (SIF) of elbows was proposed, and the influence of the wall thickness and the bend radius on the elbow stress distribution was studied. The results showed that pipeline displacement significantly affects stress for pipe bends, the stress of the elbow increased with in-plane displacement load. To ensure structural integrity for reliable working conditions for piping components, pipe displacement needs to be considered when designing bends. On this basis, a modified formula for calculating the SIF of in-plane elbow is proposed. Compared with the ASME code formula, this formula is closer to the actual stress value of the elbow due to considers the influence of pipe displacement on elbow stress. The stress value of the elbow obtained by finite element analysis essentially in agreement with the experimental value, and the average error is less than 5.16%. With simultaneous increase in bend radius and wall thickness there is a reduction in SIF. When either of the above parameters is increased on, and keeping others constant the SIF decreases. The influence of pipeline displacement on SIF is more for short bend radius and its effect decreases with increased bend radius.