By　applying　a　moving　load　with　the　uniform　velocity,　this　paper　investigates　nonlinear　behaviors　of　a　shallow　arch　model　allowing　for　describing　the　effects　of　the　initial　configuration　of　the　structure.　Two　different　cases　are　taken　into　account,　namely,　simultaneous　primary　resonances　of　the　first　and　third　modes;　simultaneous　resonances　of　the　first　mode　for　two-term　excitations.　First,　nonlinear　ordinary　differential　equations　(ODEs)　of　the　shallow　arch　are　derived　by　using　Galerkin　method.　Through　introducing　different　time　scales,　the　ODEs　are　solved　based　on　the　widely　utilized　method　of　multiple　time　scales　(MMTS).　In　this　way,　the　modulation　equations　for　the　two　cases　are　derived,　on　the　basis　of　which　the　steady　state　frequency-　and　force-response　curves　are　obtained.　Meanwhile,　phase　portraits,　power　spectra　and　two-parameter　bifurcation　diagram　are　also　given　to　assist　in　analysis　on　nonlinear　behaviors.　The　results　show　that　the　large　vibration　of　the　shallow　arch　under　the　moving　load　may　occur　and　primary　resonance　peaks　of　the　different　modes　are　located　in　distinct　positions.　©　2024　Elsevier　Masson　SAS