Long-span deck-type beam-arch composite rigid frame (BACRF) bridge fully integrates the merits of arch bridges and beam bridges, and overcomes the cracking and deflection problems of continuous rigid frame bridges. As a perfect combination of beam bridges and arch bridges, the long-span deck-type BACRF bridge boasts a light structure, a strong bearing capacity, and a powerful spanning capability. From the perspective of mechanical system evolution, this paper theoretically analyzes the structural mechanics of the beam-arch composite system, establishes a half-bridge model for BACRF bridge, and derives the expressions of the internal force and displacement of the beam-arch composite system. Next, finite-element analysis was conducted to analyze how the variation of a single parameter, e.g., rise-span ratio, open web ratio, and side-to-middle span ratio, affects midspan displacement, arch-beam junction displacement, main beam bending moment, and main arch axial force. Finally, the calculation formula for deflection-span ratio of BACRF bridge was proposed based on the maximum hyperplane method. The research results provide a reference for the structural design of similar bridges.