Mechanical loss (internal friction) experiments were applied to study the local crystallographic structure of atomic defects in cubic zirconia. Specimens (dimensions 40 x 5 x 1 mm3) with different orientation of the longitudinal axis ([100], [110], [1111) were prepared from cubic crystals stabilized with 10 mole % Y2O3 or 16 mole % CaO and measured in torsional (f almost-equal-to 1 Hz) or flexural oscillations (f almost-equal-to 1 kHz). A composite loss maximum consisting of two submaxima is observed: I (almost-equal-to 410 K) and I(A) (almost-equal-to 510 K) in ZrO2-Y2O3; I(A)'(almost-equal-to 430 K) and I(A)'(almost-equal-to 515 K) in ZrO2-CaO (f almost-equal-to 1 Hz). The peak heights of maxima I and I' depend on specimen orientation as expected for a defect of trigonal ([111]) symmetry. This strongly points to oxygen vacancies located at nearest-neighbour sites close to the dopant atoms which form elastic (and electric) dipoles, i.e. (V(o)Y'(Zr))-degrees or (V(o)Ca'') pairs, which are aligned parallel to [111] directions. The shape factor of the strain ellipsoid of the dipoles characterizing the anisotropy and strength of the local atomic displacements was determined as deltalambda almost-equal-to 0.12 - 0.14 for yttria-stabilized and deltalambda almost-equal-to 0.05 for calcia-stabilized zirconia. Loss maxima I(A) and I(A)' are assigned to larger clusters of oxygen vacancies with two or more dopant atoms.