The parametric investigation discloses influence of uncertain material parameters on stochastic earthquake response of historic masonry bridges subjected to random ground motion. Kurt Bridge, located in Samsun, Turkey is selected for numerical calculations. The east-west component of the Kocaeli earthquake in 1999, Turkey is selected as ground motion. For random ground motion, the power spectral density function is applied to each support point of three-dimensional finite element model of the historic masonry bridge. The uncertain material parameters of interest are the Elastic modulus, Poisson's ratio and mass density, which are modeled using normal, log-normal and Gumbel distributions. ANSYS finite element program is used to present the probabilistic analysis of the historic masonry bridge according to Monte Carlo Simulation results which are obtained through Response Surface Method. In this study, the central composite design for three variables is chosen as a sampling method to obtain unknown coefficients. In order to estimate the probabilistic response of the bridge, obtaining the simulation number with the exact solution through Monte Carlo Simulation, determining the type of statistical distribution are carried out. Finally, the effects of the coefficient of variation and uncertainties in material parameters on the stochastic dynamic response of the bridge are investigated. Probabilistic one standard deviation of the displacement and Von Misses stress responses are presented and compared with those of deterministic method in terms of material parameter. (C) 2016 Published by Elsevier Ltd.