The strain rate and strain rate history effects on the inelastic stress-strain behavior of annealed A-36 structural steel at room temperature is examined experimentally under monotonic and cyclic loading conditions. The strain rates used are between 10** minus **6/sec and 10** minus **1/sec, which cover the range of the strain rate that might be experienced by steel building frames during earthquake ground motions. An axial-torsional electro-hydraulic servo-controlled testing system with strain control is used for all the tests. Test results show relatively more significant strain rate sensitivity of the material for monotonic loading, and less significant strain rate sensitivity for cyclic loading. Strain rate history effect is not observed to be significant in most of the tests. The results suggest that rate-independent plasticity theories should be modified to account for the strain rate effect in certain earthquake engineering applications.