Earlier literature used elasto-plastic model for numerical modeling of friction dampers. However, the friction phenomenon is velocity dependent and elasto-plastic model is displacement dependent. Hence, their equivalence is not obvious and not established based on a systematic study. The present study evaluates three modeling approaches for friction dampers – (a) rigidly connected damper (b) friction component and spring in series and (c) elasto-plastic model. The response is calculated and compared for harmonic and earthquake excitations. Frequency response and response spectra are used to see effect of friction damper on response of SDOF. It is observed that the response of the systems have a higher sensitivity to the stiffness of the friction damper only upto a specific value. It is also shown that the optimum value of the slip load of the friction damper cannot be dependent on only system properties or only ground motion characteristics as considered in earlier literature.