What type of seismic wave moves the ground up and down or side to side?

The type of seismic wave that moves the ground up and down or side to side is the S wave, also known as a secondary wave or shear wave. This wave is characterized by its ability to move rock particles perpendicular to the direction of wave propagation, which results in an up-and-down or side-to-side motion. S waves can only travel through solids and not through liquids or gases, which differentiates them from other types of seismic waves.

In contrast, P waves (primary waves) are compressional waves that move materials back and forth in the same direction as the wave travels, pushing and pulling the rock. Surface waves, which include Rayleigh waves, travel along the Earth's surface and typically cause more damage during an earthquake because of their amplitude and motion. Rayleigh waves specifically create a rolling motion, somewhat similar to ocean waves, but they are not classified solely as moving the ground up and down or side to side. Thus, S waves effectively represent the motion described in the question.