The ultimate carrying capacity of axially loaded welded square box section members made of medium and high strength steels (nominal yield stresses varying from 345 MPa to 460 MPa), with large width-to-thickness ratios ranging from 35 to 70, is analyzed by finite element method (FEM). At the same time, the numerical results are compared with the predicted results using Direct Strength Method (DSM), modified DSM and Effective Yield Strength Method (EYSM). It shows that curve a, rather than curve b recommended in Code for design of steel structures GB50017-2003, should be used to check the local-overall interaction buckling strength of welded square section columns fabricated from medium and high strength steels when using DSM, modified DSM and EYSM. Despite all this, EYSM is conservative. Compared to EYSM and modified DSM, DSM provides a better prediction of the ultimate capacities of welded square box compression members with large width-thickness ratios over a wide range of width-thickness ratios, slenderness ratios and steel grades. However, for high strength steels (nominal yield strength greater than 460 MPa), the numerical and existent experimental results indicate that DSM overestimates the load-carrying capacities of the columns with width-thickness ratio smaller than 45 and slenderness ratio less than 80. Further, for the purpose of making it suitable for a wider scope, DSM has been modified (called proposed modified DSM). The proposed modified DSM is in excellent agreement with the numerical and existing experimental results.