Depending on the plastic deformation capacity required, structural steel design under the current codes can be classified into three categories: elastic, plastic, and seismic design. Most of the current steel codes explicitly forbid the use of a steel material with a yield strength higher than 450 MPa in the plastic design because of the concerns about its low plastic deformation capacity as well as the lack of test data on local and lateral torsional buckling behavior. In this study, flexural tests on full-scale H-shape members built with SM490A (ordinary steel or benchmark material) and HSB800 (high-strength steel) were carried out. The primary objective was to investigate the appropriateness of extrapolating the local buckling criterion of the current codes, which was originally developed for normal-strength steel, to the case of high-strength steel. All the SM490A specimens performed consistently with the current code criteria and exhibited sufficient strength and ductility. The performance of the HSB800 specimens was also very satisfactory from the strength perspective; even the specimens with a noncompact and slender flange developed the plastic moment capacity. The HSB800 specimens, however, showed an inferior plastic rotation capacity due to the premature tensile fracture of the beam bottom flange beneath the vertical stiffener at the loading point. The plastic rotation capacity that was achieved was less than 3 (or the minimum level required for a plastic design). Although the test results in this study indicate that the extrapolation of the current flange local-buckling criterion to the case of high-strength steel is conservative from the elastic design perspective, further testing together with an associated analytical study is required to identify the causes of the tensile fracture and to establish a flange slenderness criterion that is more appropriate for high-strength steel.