To study the buckling of bionics skew plates in the crane’s vein box girder,the dimensionless derivations of bucking balance differential equations for skew plates has been given when it is affected by the longitudinal load in the oblique coordinate,and the dimensionless equation of boundary conditions is also given. The calculation procedures are described in detail when the differential quadrature methods（ DQM） are used to solve the critical buckling load of simply supported skew plates. Finally,the elastic skew plate subjected to uniaxial loading condition is considered as the case study,and the DQM results are compared with the existing results to verify the accuracy of numerical solution procedures. At the same time,the affecting relation between the critical buckling load and structure parameters for the crane is discussed.