This research work deals with a stochastic approach using the entropy maximum principle to investigate the effect of parameters uncertainties on the arterial pressure. Motivated by a composite constitutive law with collagen fiber families [1], a set of uncertain parameters describing the mechanical behavior of the artery wall was considered. On the light of the available information, probability density functions were considered for the random variables governing the constitutive law in order to describe the dispersion of mechanical model response. Numerous realizations were performed according to the probability distributions and the corresponding arterial pressure results were compared to human non invasive clinical data recorded over a mean cardiac cycle. To prove the convergence of the probabilistic model, simulations of Monte Carlo were performed [2]. The different realizations were useful to define a reliable confidence region in which the probability to have a realization is equal to 95%. The obtained results demonstrate that the error in the estimation of the arterial pressure can reach 35% when the estimation of model parameters is subjected to an uncertainty ratio of 5%. Eventually, a sensitivity analysis was performed to discuss the influence of every uncertain parameter on the arterial pressure to identify the main parameters which contribute significantly in the constitutive law for a better understanding and characterization of the arterial wall mechanical behavior.