<p>This work proposes a cono-spherical indentation method for characterizing the parameters of Mooney-Rivlin and Arruda-Boyce constitutive models in rubber-like hyperelastic materials. The cono-spherical indentation model (CSIM) is formulated based on the principle of equivalent energy to establish a relationship between load-depth responses and constitutive model parameters. This model enables the efficient, in-situ and non-destructive properties characterization of hyperelastic materials during service conditions. Validation of CSIM is performed through extensive finite element simulations covering a broad spectrum of hyperelastic constitutive parameters, encompassing the Mooney-Rivlin and Arruda-Boyce models. The constitutive model parameters for four rubber-like materials are inversely identified from load-depth curves obtained through cono-spherical indentation using CSIM, and stress-stretch curves are derived from the inversely identified parameters. The accuracy of the reverse-predicted results is confirmed by comparing them with results from uniaxial tensile tests conducted over a wide range of deformations. These results highlight the efficacy of CSIM, utilizing the Mooney-Rivlin and Arruda-Boyce constitutive models, as a precise and dependable approach for predicting constitutive parameters of rubber-like materials.</p>