Laser additive manufacturing is widely used in the manufacturing and repairing of petrochemical, aerospace, and marine equipment. However, the residual stress caused by the rapid heating and cooling in the preparation of alloy materials via laser additive manufacturing likely poses a major risk of stress corrosion cracking of the material in harsh environments. This study first reviews the mechanism of residual stress in alloy materials produced via laser additive manufacturing. Second, the main measurement and elimination methods of residual stress in materials are summarized. In addition, the test methods and the mechanism of stress corrosion cracking in alloy materials caused by laser additive manufacturing are summarized. Finally, based on the research status of residual stress and stress corrosion cracking of alloy materials in laser additive manufacturing, the key problems that need to be solved in this field and future development trends are summarized.