Due to the different lifting points of non-standard girders compared to standard girders during the lifting process, the stress situation and the potentially weakest position of the bridge erecting machine change accordingly. For ensuring the safety of the bridge erecting machine during the lifting process, it is necessary to analyze the stress characteristics of the bridge erecting machine and provide local reinforcement suggestions for the most unfavorable stress position. With the hoisting of a 35 m non-standard girder for the Luoxizhou Bridge project as the engineering background, Midas Civil was used for a finite element analysis to numerically simulate the stress states of the bridge erecting machine under different working conditions during the lifting process. The deflection and stress results of the bridge erecting machine beam were analyzed to determine its most unfavorable load working condition. In addition, considering that the overhead crane is unconstrained laterally when moving on the beam, which may lead to lateral instability of the bridge erecting machine under eccentric load, it is also necessary to analyze its overall buckling strength and local stability under the most unfavorable working condition. The results show that under the most unfavorable load, the maximum stress of the main beam of the bridge erecting machine is 140.4 MPa, and the maximum vertical deformation is 44.4 mm. Compared with those in the case of lifting a 32 m standard girder, the maximum vertical deformation increases by nearly 12%, and the maximum stress increases by about 8%. The overall stability safety factor of the bridge erecting machine is 12.8, and the local stability factor is much smaller than the overall stability safety factor. To ensure the local stability of the web members of the bridge erecting machine, local reinforcement should be adopted by adding web members to the middle section to prevent local buckling instability of the web members.