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We present a parameter identification procedure developed for a composite model of arterial wall which is characterized by collagen viscoelastic fibres embedded in hyperelastic incompressible matrix. The structure undergoes large deformation described using the total Lagrangian formulation. In the paper the identification procedure is tested numerically when applied to a simulated vessel dynamic inflation test, which can be performed in vivo. A stability test of the identification method is pursued as illustrated by two examples: the creep and relaxation tests.