While most bridges feature multiple spans, limited theoretical research has addressed vehicle-bridge interaction on continuous spans, especially involving two-axle vehicles. This study presents analytical solutions for a two-span continuous bridge interacting with a three-mass test vehicle, aimed at identifying bridge frequencies via the vehicle scanning method. Both the vertical and rotational responses of the test vehicle are analytically derived. Key findings include: (1) accurate bridge frequency identification at low vehicle speeds; (2) symmetric and antisymmetric mode shapes in equal-span bridges for even and odd modes, respectively; (3) strong agreement between analytical and finite element results in capturing closely spaced modes. These insights contribute to the development of reliable, drive-by bridge monitoring techniques.