Compressive creep of dense polycrystalline $BaTiO_3$, with average grain sizes of 19.3-52.4$mu extrm{m}$, has been investigated at 1100-$1300^{circ}C$ in air or under controlled atmospheres $(10^2-10^5Pa ;O_2)$. Some cavity growth occurred during deformation because of non-steady-state damage accumulation in the form of cavitation. Comparison of the creep data of polycrystalline BaTiO3 with existing diffusivity and creep data for perovskite oxides suggested that deformation of polycrystalline $BaTiO_3$ was controlled by the extrinsic lattice diffusion of barium or titanium.