In this study, the effect of the high frequency components of near fault ground motions (NFGM) with forward rupture directivity effect (FRDE) on the seismic response of elastic and inelastic SDOF regular (non-isolated) and seismic isolated structures is studied. For this purpose, Moving Average filtering method is used to remove the high frequency content of the NFGM at various filtering levels. The key motive for this effort is to evaluate the appropriateness of representing the NFGMs by decomposed signals or mathematical pulse waveforms. Then, elastic and inelastic SDOF structures with various properties are subjected to the original and filtered NFGM and the responses are compared via elastic and inelastic response spectra. In addition, the efficiency of several pulse models in simulating the actual effect of NFGM on the seismic response of elastic and inelastic SDOF structures is investigated. The analyses results revealed that the high frequency content of NFGM has a significant effect on short period elastic structures and inelastic structures with high yield strength subjected to NFGM with short pulse periods. Furthermore, it is found that popular pulse models available in the literature failed to simulate the effect of the actual NFGM on the response of elastic and inelastic structures.