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In this work the mechanical response of hyper-elastic spherical membranes subjected to dynamic inflation is revisited. Specifically, a comprehensive analysis on the role that the constitutive behaviour of the material has on the mechanical stability of the membrane has been developed. Six different strain-energy functions, frequently used to approximate the constitutive behaviour of elastomeric solids, have been considered: three of the Mooney-Rivlin class and three of the Ogden class. For all the constitutive models used, the material parameters have been obtained from Bucchi and Hearn (2013a, 2013b), where the same set of experimental results was used to calibrate the models. We show that essential features of the dynamic response of the spherical shell are closely related to the strain-energy function selected to describe the constitutive behaviour of the membrane. As reported by Bucchi and Hearn (2013a, 2013b), this issue is frequently overlooked within the literature since too often only one strain-energy function is used to address this type of dynamic problems. (C) 2015 Elsevier Ltd. All rights reserved.