Optimizing the productivity of nonconventional, low-permeability “shale” reservoirs requires detailed knowledge of the mechanical properties of such materials. These rocks' elastic anisotropy is acknowledged but usually ignored due to difficulties in obtaining such information. Here we study in detail the dynamic and static elastic properties of a suite of calcareous mudstones from the nonconventional Duvernay reservoir of Alberta, Canada. The complete set of transversely isotropic elastic constants is obtained from strategically oriented ultrasonic transducers to confining pressures of 90 MPa. Wave speed anisotropies of up to 35% are observed at even the highest confining pressures. Furthermore, the stress sensitivity of the wave speeds, and hence moduli, is itself highly dependent on direction with speeds taken perpendicular to the bedding plane being highly nonlinearly dependent on pressure, whereas those along the bedding plane show, unexpectedly, nearly no pressure dependence. These observations are in qualitative agreement with the preferentially oriented porosity and minerals seen in scanning electron microscope images. These results may be significant to the interpretation of sonic logs and azimuthal amplitude versus offset for principal stress directions, for the concentration of stress within such formations, and for estimation of static engineering moduli from sonic log wave speeds.