In this paper, a probabilistic approach is adopted to determine material parameters. The proposed algorithm is tested to estimate material parameters of tubular materials subjected to a spherical punch test. We assume the measured Force-Deflection (F-D) data, Major Strain-Deflection (MS-D) and anisotropy parameters are corrupted with a Gausian noise σ=1% and σ=4% and zero mean at the all data points. Then we employ a Markov chain Monte Carlo (MCMC) method in a Bayesian framework to solve the inverse material parameter identification problem. The results show how uncertainty of the measurement values influence the uncertainty of the estimated material parameters. This approach can be adopted to study stability of the inverse problem in the presence of the experimental noise.