In order to overcome the local buckling instability of skew plates in box girder,the equations of momentof simply-supported edges in oblique coordinate system and the buckling differential governing equations of skewplates subjected to longitudinal in-plane loads are deduced.Then,by combining the harmonic differential quadraturemethod with the build-in method,a novel method to implement the critical buckling stability of simply-supportedskew plates is proposed. Moreover,by taking the skew plates subjected to uniaxial pressure or shear force as astudy sample,the influences of load-varying coefficient,aspect ratio and skew angle on the critical bulking load areinvestigated. The results show that,when the simply-supported skew plates are subjected to uniaxial pressure,thecritical buckling load increases with the increase of load-varying coefficient and with the decrease of skew angle,however,it undergoes a decrease during its increase with the aspect ratio. Moreover,it is found that,when theskew plates are subjected to shear force,the critical buckling load increases with the aspect ratio,and that it firstdecreases and then increases with the increase of skew angle.