The pressure dependence of the static magnetic susceptibility χ(T) of the heavy-electron superconductor UBe13 was investigated over temperatures ranging from 1.5 to 300 K and at pressures from 1 bar to 8 kbar. It is linear in pressure over the full temperature range, having a small constant pressure dependence at higher temperatures that increases rapidly below about T=150 K. The maximal value of the relative susceptibility change [1/χ(dχ/dP)] is about 1% per kbar. The Curie-Weiss law is obeyed in the temperature range 100 to 300 K with the effective magnetic moment peff=3.46μB independent of pressure, while the paramagnetic Curie temperature FTHETA∼-100 K becomes more negative with pressure. The lattice parameter of cubic UBe13 was measured as a function of pressure, permitting a determination of a compressibility value of -9.2×10-4 kbar-1 near ambient pressure. The pressure dependence of χ(T) is significantly weaker than that of the specific-heat coefficient C(T)/T; we discuss whether this can be resolved by (i) consideration of intersite antiferromagnetic interactions, or (ii) the quadrupolar Kondo-effect model, and conclude that the latter provides a stronger explanation of the results. © 1993 The American Physical Society.