In　this　study,　a　genetic　algorithm-based　(GA-based)　method　for　the　estimation　of　the　parameters　in　the　finite　mixture　distributions　is　proposed　and　applied　to　the　multi-modal　modeling　of　the　stress　spectrum　of　a　typical　welded　joint　of　Tsing　Ma　Bridge.　Firstly,　the　temperature　effect　on　the　original　strain　monitoring　data　is　eliminated　by　wavelet　transform.　The　rainflow　counting　algorithm　is　employed　to　transfer　the　strain　stress　histories　into　daily　stress　spectra.　A　standard　daily　stress　spectrum　accounting　for　highway　traffic,　railway　traffic,　and　typhoon　effects　is　derived.　Then,　the　multi-modal　modeling　of　the　stress　range　is　conducted　by　use　of　three　types　of　finite　mixture　distributions　(normal,　lognormal,　and　Weibull)　in　conjunction　with　the　GA-based　mixture　parameter　estimation　method.　The　optimal　finite　mixed　model　is　determined　by　the　Akaike＇s　information　criterion　(AIC).　Finally,　the　joint　probability　density　function　(PDF)　of　the　stress　range　and　the　mean　stress　is　obtained　using　the　bivariate　finite　mixture　distributions　and　the　GA-based　mixture　parameter　estimation　method.　The　results　show　that　the　proposed　GA-based　mixture　parameter　estimation　method　is　adequate　in　the　probabilistic　modeling　of　two　random　variables.