Near-fault ground motion with directivity or fling effects is significantly influenced by the rupture mechanism and substantially different from ordinary records. This class of ground motion has large amplitude and long period, exhibits unusual response spectra shapes, possesses high PGV/PGA and PGD/PGA ratios and is best characterized in the velocity and the displacement time-histories. Such ground motion is also characterized by its energy being contained in a single or very few pulses, thus capable of causing severe damage to the structures. This paper investigates the characteristics of near-fault pulse-like ground motions and their implications on the structural responses using new proposed measures, such as, the effective frequency range, the energy rate (in time and frequency domains) and the damage indices. The paper develops also simple mathematical expressions for modeling this class of ground motion and the associated structural responses, thus eliminating numerical integration of the equations of motion. An optimization technique is also developed by using energy concepts and damage indices for modeling this class of ground motion for inelastic structures at sites having limited earthquake data.