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Cosmological $\alpha$-attractors are observationally favored due to theasymptotic flatness of the potential. Since its flatness induces the negativepressure even after inflation, the coherent oscillation of the inflaton fieldcould fragment into quasi-stable localized objects called I-balls (or"oscillons"). We investigated the possibility of I-ball formation in E-modelsof $\alpha$-attractors. Using linear analysis and the lattice simulations, wefind that for $\alpha\lesssim10^{-3}$, the inflaton feels the negative pressurelong enough and actually fragments into I-balls.

Inflaton fragmentation in E-models of cosmological $\alpha$-attractors