Simulation of fibre-reinforced hyperelastic models characterising rubbers, fibre-reinforced elastomers, and biological soft tissues (e.g. arteries), in optimization processes for designing flexible aircraft structures or biomedical structures, can be inaccurate due to numerical instability. This instability problem is caused by the ill-conditioned constitutive matrix of the model, leading to unphysical behaviour. This paper further investigates the problem for a hyperelastic model in which the fibres characterised by a 2D Fung-type potential and an isotropic term representing the matrix, namely the modified Fung-type model (MFH). The unrealistic response of the convex MFH might take place in physiological range of soft tissues or in interested range of hyperelastic materials. To analyze this instability, several tension tests are conducted with the material constants of the MFH obtained from curve fitting to experimental data of arterial samples by G. A. Holzapfel. These tests resulted in poor stress solutions associated with unrealistic thickness thickening of the tested specimens. Consequently, the paper proposes a novel Fung-type potential that overcomes this numerical instability so that the model can ensure physical response in the physiological deformation range of the artery
