Space folding techniques based on non-monotonic transforms lead to a new class of 2D isotropic cloaks with a constant negative shear modulus and a spatially varying negative density for antiplane elastic waves. We consider an external cloak consisting of a core with positive shear modulus and density, and a shell with simultaneously negative shear modulus and density. Such a core–shell resonant system creates a virtual folded region outside the shell. To handle such negative physical parameters in the time-domain, a two-step strategy is used: (i) assuming resonant (Drude and Lorentz-types) effective parameters in the frequency-domain; (ii) returning to the time-domain by applying the formalism of the auxiliary fields. We numerically show that, at the designed central frequency, scattering of a cylindrical antiplane elastic wave incident upon a finite set of small clamped obstacles is drastically reduced after a lapse of time, when they are placed in the close neighborhood of the external cloak. However, cloaking efficiency decreases when the source is placed in the intense near field of the external cloak and moreover at short times, cloaking breaks down.