IEEE　As　a　consequence　of　industrial　development,　large　quantities　of　hazardous　materials　are　shipped　everyday.　Most　related　studies　consider　the　risks　as　fixed　weights　on　edges.　However,　the　loads　of　the　vehicles　are　important　factors　about　the　risks.　Thus,　considering　the　risks　as　fixed　parameters　cannot　reflect　actual　practice.　In　addition,　the　vehicle　routing　models　in　previous　studies　simultaneously　minimize　the　total　transportation　cost　and　the　total　risk.　However,　simply　considering　the　total　risk　of　a　fleet　as　a　whole　cannot　evaluate　each　vehicle's　risk.　Although　the　total　risk　is　low,　the　risk　of　a　specific　vehicle　may　still　be　very　high.　In　this　paper,　the　actual　load　dependent　risk　is　introduced,　and　a　corresponding　bi-objective　vehicle　routing　model　for　hazardous　materials　transportation　is　developed,　minimizing　the　maximum　risk　of　vehicles　and　the　total　transportation　cost　simultaneously.　An　exact　algorithm　is　developed　based　on　the　＜formula＞＜tex＞$\varepsilon　$＜/tex＞＜/formula＞-constraint　method　with　several　improvements.　For　large-scale　problems,　an　approximation　approach　is　proposed.　Computational　experiments　on　a　series　of　instances　are　reported　and　several　managerial　insights　are　derived　from　the　sensitivity　analysis.