The scope of this study is the quantification of vertical peak floor acceleration demands at column lines and along the length of beams of elastic moment-resisting steel frames subjected to recorded ground motions. These demands correlate with the maximum strength demands on rigid nonstructural components attached to a frame structure. Since it is commonly assumed that buildings behave flexibly in the horizontal direction and rigidly in the vertical direction, the assessment of vertical acceleration demands is typically not considered in most cases. The results of this study show that vertical peak floor accelerations can be up to five times larger than the vertical peak ground acceleration, in contrast to horizontal peak floor accelerations that are only up to two times larger than the horizontal peak ground acceleration for the numerical models used in this study. The most significant amplifications estimated in the vertical direction are found at the center of the girders. Further investigations of modified steel frames indicate that the story-wise mass distribution has an influence not only on the vertical acceleration demand, but also on the horizontal component of the response, though to a lesser degree. In contrast, the response in the vertical and horizontal direction is only slightly affected by an increase in the flexural stiffness of the beams. The results of this study strongly indicate that in steel frames it can be considered highly questionable to ignore the amplification of the vertical acceleration component along the height of the structure.