The high pressure properties of the novel tetrel-free clathrate, Ba8Cu13.1Zn3.3P29.6, were investigated using synchrotron powder X-ray diffraction. The pressure was applied using a diamond anvil cell. No structural transitions or decomposition were detected in the studied pressure range of 0.1–7 GPa. The calculated bulk modulus for Ba8Cu13.1Zn3.3P29.6 using a third-order Birch-Murnaghan equation of state is 65(6) GPa at 300 K. This bulk modulus is comparable to the bulk moduli of Ge- and Sn-based clathrates, like A8Ga16Ge30 (A = Sr, Ba) and Sn19.3Cu4.7P22I8, but lower than those for the transition metal-containing silicon-based clathrates, Ba8TxSi46−x, T = Ni, Cu; 3 ≤ x ≤ 5.