Publisher Summary This chapter presents a paper that describes a study on floor acceleration demands of the moment frame buildings subjected to earthquake ground motion. Recently, a method developed by the authors to estimate the floor acceleration demands on buildings with linear elastic behavior when subjected to earthquake ground motions. Most of the studies on accelerations have been carried out in relation to nuclear power plants. The model of a multistorey building is subjected to ground motions with increasing the level of intensity. The peak values of absolute and relative floor accelerations can be presented as a function of ground motion intensity. This paper explains the saturation of acceleration and the correlation between ground motion and relative floor accelerations. It evaluates the correlation between nonlinear and linear response for a wide range of ground intensities. There is a need to develop simplified methods to estimate floor acceleration demands when the structures behave nonlinearly. This paper addresses some aspects of nonlinear floor accelerations, which provide useful information for those methods to be developed.