Static-compression experiments to 59 GPa (590 kbar), employing X ray diffraction through a diamond cell, demonstrate that strontium oxide (SrO) transforms from its initial B1 (NaCl-type) to the B2 (CsCl-type) structure at 36 (¿4) GPa on the ruby fluorescence scale with a volume change at the transition ΔV/V1~-13%. These results confirm earlier predictions based upon systematics for oxides but are in lesser agreement with ab initio (modified electron gas) claculations. The new data for the B1 phase are consistent with previous ultrasonic and static-compression measurements, which indicate that K'0 >4. Data spanning the 25-GPa range in pressure constrain the equation of state of the B2 phase. The change in bulk sound velocity at the transition is shown to be essentially zero, which is a significant deviation from the behavior predicted by velocity--density systematics.