The rapidly oscillating Ap stars (roAp) are a class of nonradially pulsating stars oscillating in low-degree modes with periods of 4–15 minutes. We have started a program to study the oscillations on several roAp stars using precise radial velocity (RV) measurements. The typical mean RV amplitude for the roAp stars we have observed is 50–400 ms−1, but this amplitude depends on the spectral region used for the measurement of the RV amplitude. A detailed line-by-line analysis reveals that the pulsational amplitude depends not only on atomic species, but on the line strength as well. For a given atomic species weak spectral lines exhibit a pulsational amplitude 10–100 times higher than for strong lines. The elemental effect can be understood in the context of the inhomogeneous distribution of elements known to occur on these stars and that is believed to result from the global dipole magnetic fields that are present. For instance, if an element is concentrated near the magnetic pole then it may have a higher RV amplitude than one that is distributed about the magnetic equator. The line strength effect is interpreted as arising from vertical structure to the pulsations since weaker lines are formed, on average, deeper in the atmosphere than stronger lines. Precise RV measurements may prove to be a powerful tool for probing both the vertical and horizontal structure of the pulsations in roAp stars.