Application of the scaled fundamental equation of state of Balfour et al. (Phys. Lett. A, vol. 65, 1978, pp. 223–225) based upon universal critical exponents, demonstrates that there exists a bounded thermodynamic domain, located within the vapour–liquid equilibrium region and close to the critical point, featuring so-called negative nonlinearity. As a consequence, rarefaction shock waves with phase transition are physically admissible in a limited two-phase region in the close proximity of the liquid–vapour critical point. The boundaries of the admissibility region of rarefaction shock waves are identified from first-principle conservation laws governing compressible flows, complemented with the scaled fundamental equations. The exemplary substances considered here are methane, ethylene and carbon dioxide. Nonetheless, the results are arguably valid in the near-critical state of any common fluid, namely any fluid whose molecular interactions are governed by short-range forces conforming to three-dimensional Ising-like systems, including, e.g. water. Computed results yield experimentally feasible admissible rarefaction shock waves generating a drop in pressure from 1 to 6 bar and pre-shock Mach numbers exceeding 1.5.