During the construction of parallel swivel bridges, the stress state of the spherical hinge under load is crucial. The stress results of the spherical hinge are of great significance to the subsequent structural design and even the safety and stability of the bridge structure. The refined finite element model of the spherical hinge was established using ABAQUS software. The vertical displacement and local stress state of the spherical hinge under vertical load were analyzed and discussed. The results indicate that the maximum principal compressive stress is less than the allowable stress and meets the requirements. When the spherical hinge is only subjected to the upper static load, the vertical stress of the upper and lower steel spherical hinges gradually increases along the center of the spherical hinge to the edge, in which the vertical stress at the edge of the spherical hinge is the largest and the stress of the lower spherical hinge is slightly smaller than that of the upper spherical hinge. The maximum compressive stresses of the upper spherical hinge and the lower spherical hinge are 63.89 MPa and 54.24 MPa, respectively. Under the upper static load, the displacements of the upper and lower spherical hinges are very small, with maximum displacements of 0.234 mm and 0.202 mm, respectively, thus meeting the design requirements.