Abstarct: Abstract ................................................ Bridges are designed to withstand a variety of loads including dead, live, environmental, and occasional loads during their service life. In monitoring the structural health of bridges, methods baxsed on vision, weight in motion, weight in motion of the bridge, drive-by, and models baxsed on bridge-vehicle interaction are the methods that are generally used. Therefore, the main goal of this thesis is to extract the relationship between the single-span vertical arch bridge and the vehicle passing over it. baxsed on this, the modeling was first coded in MATLAB software using the finite element method, and the bridge and car interaction model was applied to it. Then, the effect of radius changes on the bridge parameters, including vertical and horizontal displacement and rotation in the degrees of freedom of the baxse points (points 1⁄4, 1⁄2 and, 3⁄4 of the le ngth of the beam span) has been investigated. Validation of the provided relationships has been done in two ways. After validating the obtained equation, by using the signals obtained from the wheel of the car (changing the location of different points of the bridge), the frequencies and damping ratios and the shape of the vibration modes have been extracted by the random subspace identification method. In the end, the reliability of the used identification method is measured with Moody's confidence criterion. In the single-span vertical arch bridge system, identification of the bridge structure system for different radii, by comparing and checking the results of two FEM and SSI methods, it is possible to mention the high reliability and efficiency of the random subspace identification method. The output of the obtained results indicates the high efficiency and reliability of the random subspace identification method in extracting the modal parameters of the bridge structure system.