We report on the mechanical loss from bulk and shear stresses in thin film, ion beam deposited, titania-doped tantala. The numerical values of these mechanical losses are necessary to fully calculate the Brownian thermal noise in precision optical cavities, including interferometric gravitational wave detectors like LIGO. We found the values from measuring the normal mode mechanical quality factors, Q ’s, in the frequency range of about 2000-10,000 Hz, of silica disks coated with titania-doped tantala coupled with calculating the elastic energy in shear and bulk stresses in the coating using a finite element model. We fit the results to both a frequency independent and frequency dependent model and find φshear = (8.3 ± 1.1) × 10−4 , φbulk = (6.6 ± 3.8) × 10−4 with a frequency independent model and φshear (f)=(5.0±0.7)×10−4 +(5.4±1.1)×10−8 f, φbulk (f)=(11±2.8)×10−4 −(8.7±4.7)×10−8 f with a frequency dependent (linear) model. The ratio of these values suggest that modest improvement in the coating thermal noise may be possible in future gravitational wave detector optics made with titania- doped tantala as the high index coating material by optimizing the coating design to take advantage of the two different mechanical loss angles.