Aiming at the problem of the brittle fracture of pressure pipeline, the elastic constraint structure is described by using members and engineering building structures, and the concept of elastic constraint is proposed. Through the stress field analysis of the pressure pipeline under internal pressure, it is found that the pressure pipeline under internal pressure is an elastic constraint structure. The elastic constraint effect is applied to the pressure pipeline to explore the influence of elastic constraint effect on the brittle fracture of pressure pipeline. The critical wall thickness and limit load of different materials are calculated by the limit bearing formula. Through simulation analysis of materials with different yield ratios and pipelines with different wall thicknesses of the same material (yield ratio is the ratio of yield strength to tensile strength), it was found that pressure pipelines made of the same material have an increased load-bearing capacity as the wall thickness increases, but their own elastic constraint effects are becoming more obvious, and the probability of the brittle fracture of the pipeline is higher. When the wall thickness of pressure pipelines made of materials with different yield ratios is certain, the lower the yield ratio is, the more likely the pipeline is to generate plastic deformation and the larger the deformation capacity is; the higher the yield ratio, the poorer the plastic deformation capacity of the pipeline and the smaller the deformation capacity. Pipelines with large yield ratio are more sensitive to the brittle fracture than those with small yield ratio.