This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular system based on stochastic simulation of a one dimensional arterial network. A general analysis of different uncertainties and probability characterization with log-normal distribution of these uncertainties is introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish the stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe the blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation method with sparse grid technique, we study systemically the statistics and sensitivity of the solution with respect to many different uncertainties in a relatively complete arterial network with potential physiological and pathological implications for the first time.