The concept of nondiffracting waves is generalized to encompass bulk-acoust
ic waves within crystalline media. We introduce acoustic Bessel beams and g
eneralized X waves for anisotropic elastic materials. Detailed numerical pr
edictions for propagation-invariant bulk-acoustic beams of various orders,
and also X pulses, are presented for experimental verification. The materia
l parameters used have been chosen appropriately for quartz, the most impor
tant material for acoustic device applications.