To assess creep-induced delayed compaction localization in rate-dependent porous rocks， a theoretical criterion for compaction localization is proposed based on elastic-viscoplasticity and the theory of controllability. By establishing systems of local ordinary differential equations， the elastic viscoplastic constitutive operator is defined under the stationary external perturbation condition to identify the unstable acceleration deformation inside the spontaneously propagating strain localized bands. By detecting the loss of controllability in the systems， an instability index for compaction localization in rate-dependent porous rocks is derived. The proposed index is verified by simulating the quasi-instantaneous and delayed compaction localization in a porous rock based on the viscoplastic constitutive model. Furthermore， the applicability of the proposed index in analyzing delayed compaction localization in boundary value problems is validated by using finite element simulation of plane strain compression tests.