This work describes x-ray absorption measurements under high pressure in ReB(2), complemented by ab initio calculations. The EXAFS analysis yields the average Re-B bond compressibility, which turns out to be χ(ReB) = 5.6(9) × 10(-4) GPa(-1). Combining this information with previous x-ray diffraction experiments we have characterized the network of covalent bonds responsible for the rigidity of the structure. The main conclusion is that the compression is anisotropic and nonhomogeneous, reflecting bonding differences between Re-B and B-B bonds and also between nonequivalent Re-B bonds. The layer defined by boron atoms tends to become flatter under high pressure. As a consequence, the structural rigidity, necessary to attain high hardness values, is compromised.