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In this paper, we have investigated the role played by the material compressibility in the oscillatory behaviour of hyperelastic spherical shells subjected to dynamic inflation. For that purpose, we carried out a comprehensive nondimensional numerical analysis using: (i) a finite differences MacCormack's scheme implemented in MATLAB, and (ii) a finite element model developed in ABAQUS/Explicit (Abaqus Explicit v6.10 user's manual, version 6.10 edn. ABAQUS Inc., Richmond, 2010). We have detected that numerical dispersion and diffusion impose limits to the capacity of the computations to describe the shock wave that emanates from the inner surface of the shell due to the application of the inflation pressure. Nevertheless, both numerical approaches capture the essential features that describe the oscillatory behaviour of the shell, including the maximum stretch of the oscillation. Using the key nondimensional groups that control the problem at hand, we have conducted a parametric study to assess the role played by nondimensional applied pressure, material compressibility, and nondimensional shell thickness in the oscillatory behaviour of the specimen. We have shown the interplay between the maximum amplitude of the oscillation and the applied pressure and obtained the critical pressure for which the oscillatory behaviour is lost, leading to an unbounded expansion of the spherical shell. Moreover, our calculations have revealed that the wave propagation within the specimen plays a key role in the dynamic response of the shell. The phase portraits used to represent the oscillatory behaviour of the spherical shell show a characteristic sawtooth form that is accentuated with the increase in material compressibility and shell thickness.