AbstractThe timing and rate of decompression melting of a compositionally heterogeneous mantle during continental rifting are assessed with a new one‐dimensional geodynamic code, MELT1D. MELT1D computes pressure and temperature in the extending lithosphere and rising asthenosphere and calculates the resulting melt fraction and eruption rates for different lithologies. A series of models simulate syn‐rift melt production from (a) dry and wet depleted lherzolite similar to the mantle that underlies most mid‐ocean ridges, (b) dry and wet relatively fertile ultramafic compositions representing plume or primitive mantle material, (c) pyroxenite representing recycled ultramafic oceanic crust or magmatic metasomes, and (d) basalt representing recycled mafic crust or metasomes. The models predict sequential melting of the different compositions that is broadly consistent with basalt eruption histories in many Phanerozoic rifts. Results show a progressive transition in magma sources as the lithosphere thins, beginning with melting of wet mantle and compositionally fertile mafic components near the lithosphere‐asthenosphere boundary during the earliest stages of extension. This transitions to magmatism dominated by melting of relatively fertile ultramafic components (pyrolitic and pyroxenitic compositions) as extension progresses, and finally to melting of ambient lherzolite asthenosphere as lithosphere thinning approaches breakup. Mantle composition, pre‐rift lithosphere thickness, and mantle temperature exert the greatest controls on the timing and volumes of magmas produced from each lithology. In general, a cool or thick lithosphere has a greater capacity to sequester fertile lithologies than thin or warm lithosphere, and thus has a greater capacity to produce early syn‐rift magmas without requiring a hot mantle plume.