We have simulated the formation and evolution of comet 1P/Halley's meteoroid stream by ejecting particles from the nucleus 5000 years ago and propagating them forward to the present. Our aim is to determine the existence and characteristics of associated meteor showers at Mars and Venus and compare them with 1P/Halley's two known showers at the Earth. We find that one shower should be present at Venus and two at Mars. The number of meteors in those atmospheres would, in general, be less than that at the Earth. The descending node branch of the Halley stream at Mars exhibits a clumpy structure. We identified at least one of these clumps as particles trapped in the 7:1 mean motion resonance with Jupiter, potentially capable of producing meteor ourbursts of ZHR∼1000 roughly once per century.