Wave propagation is a constant-fabric macrophenomenon, suitable to microinterpretation.  Both velocity and attenuation characterize state, including inherent and stress-induced anisotropy.  The purpose of this research is to study the effect of isotropic and deviatoric stresses on wave propagation in particulate materials at low strains and to interpret results at the microlevel.  A resonant-column device was modified to allow for the application of axial extension and axial compression deviatoric loading.  The fixed-free boundary condition of the sample was maintained.  Data for round, hard-grained sand show that shear wave velocity and attenuation are primarily dependent on the mean stress on the polarization plane, with minimal effect of the deviatoric component, in agreement with prior observations at stress ratios less than 2-3.  Attenuation is strongly correlated with the mean stress in the polarization plane and the level of shear strain.  Damping does not vanish at low strains, contrary to predictions based on hysteretic behavior; hence, other loss mechanisms must take place at low strains.  Low-strain wave parameters are adequately corrected for mid-strain using modified hyperbolic models.  Measured velocity and damping trends during isotropic and anisotropic loading qualitatively agree with predictions based on regular arrays.