Computational theory of axial compression bearing capacity in different national and foreign design standards are compared. The axial compression tests of Q420 high strength steel tube with different slenderness ratios are carried out. Integral instability happens during the tests, and obvious local buckle appears in the section of 1/2 length at the end of test. The bearing capacities of Q420 high strength steel tubes are calculated and compared. The calculation results agree with the testing results of the steel tubes that slenderness ratio is smaller than 60, and the test results for other slenderness ratios are lager than the calculation results. The calculation results are conservative, which are obtained according to the code for steel structure design, AIJ 1990 of Japan, S37-94 of Canada and BS EN 1993, and the computational theory could apply to the engineering design.