The stress singularity phenomenon generated by finite element analysis of engineering structures was studied, and the stress singularity suppression method was proposed. The stress singularities could be divided into geometric catastrophe stress singularity, load catastrophe stress singularity and material catastrophe stress singularity. Using ANSYS Workbench simulation platform, three typical stress singular models were established respectively, and the numerical simulation analysis was carried out. The analysis results show that the essence of the stress singularity phenomenon in the finite element analysis process is caused by structural stiffness mutation, and the stress singularity can be suppressed by modifying the model and applying the equivalent constraint.