The primary resonance and the stability of a harmonically forced oscillator with a pair of symmetric set-up elastic stops are studied by means of the average approach. It is found that the set-up elastic stops greatly increase the complexities of the primary resonance as follows. Four kinds of persistent primary resonance and three critical cases exist. The motion of many of the persistent resonances becomes unstable when it begins to touch the set-up elastic stops with decrease of the excitation frequency. Moreover, there coexist three stable periodic motions and two unstable periodic motions at certain combinations of system parameters.