Latest structure construction crafts frequent use of composite steel-concrete arches for building and bridge applications. The leading goal of this research is to describe a three-dimensional finite element model capable of describing the response of a composite steel-concrete arch. The commercial software Abaqus was implemented to develop the proposed approach, where a certain experimental test results in the literature on a scaled steel-concrete composite arch have been compared to validate the accuracy and adequacy of the proposed finite element model. Furthermore, the current research developed a finite element model to study the fundamental behavior of a composite steel box-concrete arch with a specific parameter. These parameters including the degree of curvature, the number of the shear connector, and the support conditions have been considered the main study parameters. The proposed model has presented an excellent prediction of the initial stiffness, the ultimate strength, and the ductility of the composite arch. The Representative behavior was affected significantly by the designated variable for the steel box section with composite deck. Therefore, these findings may be crafted with the aim of structural design rules.