© 2020 American Physical Society. Isolated linear carbon chains (LCCs) encapsulated by multiwalled carbon nanotubes are studied under hydrostatic pressure (P) via resonance Raman scattering. The LCCs' spectroscopic signature C band around 1850 cm-1 softens linearly with increasing P. A simple anharmonic force-constant model not only describes such softening but also shows that the LCCs' Young's modulus (E), Grüneisen parameter (γ), and strain ( µ) follow universal P-1 and P2 laws, respectively. In particular, γ also presents a unified behavior for all LCCs. To the best of our knowledge, these are the first results reported on such isolated systems and the first work to explore universal P-dependent responses for LCCs' E, µ, and γ.