Describe the motion of particles in a material when this ultrasound wave passes through?
pls , confused?
you

Yes, the particles are just moving back and forth, not moving in any particular direction on average. For one, the particles are only moving in response to the sound wave, in perfect synchronization, and they aren't also moving constantly in random directions. If you had some material that would remain a gas at absolute zero, then a sound wave in that absolute-zero gas would look more or less like it. But for an everyday-volume sound wave in room-temperature air, the random thermal motion (which is always happening whether or not there is a sound wave) is much stronger than the motion caused by the sound wave. The only reason we notice a sound wave at all is because it is an ordered motion that carries energy in a particular direction. If you followed the motion of a single air molecule, it would look entirely random and there would be no trace of the sound wave. The sound wave only becomes apparent when you look at the large-scale pattern of density variations.The other weird thing about the animation is that the molecules stop moving and turn around without colliding with anything! It should be obvious that in a real gas made of electrically neutral particles, there is no long-distance force that would cause this to happen, and a moving particle would not change direction unless it actually collided with another particle.To answer your particular questions, yes, the whole medium is "vibrating" in that the density and pressure are increasing and decreasing periodically, as the gas flows back and forth. there doesn't have to be any well-defined cross-sectional shape for the sound wave. In fact, the simplest geometry to consider is a plane wave, which extends infinitely in all directions perpendicular to the direction of propagation. It's actually impossible to make a "beam" of sound that will propagate forever without spreading out. 
So, yea. Hope that helped.