Techniques have been developed to measure the cross pressure and temperature dependence of elastic moduli of olivine using the gigahertz ultrasonic interferometric method in a gas pressure vessel (to 500 MPa) equipped with an internal heater (to 500 K). Special attention has been drawn to the effect of the bond which couples the sample to the buffer rod. We obtained ∂2G22/∂P∂T=(2.8¿0.9)¿10-3 K-1 for a San Carlos olivine sample with a lapped contact. Selective values of ∂2KT/∂P∂T (0, 0.5¿10-3, 1.0¿10-3 K-1) are used to calculate their effect on cell volume, bulk modulus, and bulk sound velocity for olivine at pressures to 14 GPa and temperatures to 1800 K (410-km depth), using the high-temperature form of the Birch-Murnaghan equation of state. The largest difference between the cell volumes for ∂2KT/∂P∂T=1¿10-3 K-1 and for ∂2KT/∂P∂T=0 is about 0.6% at the highest pressure and the highest temperature (14 GPa, 1800 K). Therefore PVT data with precision at least better than 0.6% are required to distinguish between the extreme values of ∂2KT/∂P∂T for olivine if the pressure and temperature data are free of errors. If the cross pressure and temperature derivative term is neglected (∂2KT/∂P∂T=0) in extrapolating laboratory elasticity data to mantle pressure and temperature conditions, the bulk modulus of olivine can be underestimated by as much as 10% and the bulk sound velocity by 3% at the 410-km seismic discontinuity. Thus the present study highlights the need to measure elastic properties of mantle candidate minerals at the P-T conditions of the mantle transition zone in order to establish a more precise model of the mantle mineralogy. ¿ American Geophysical Union 1996