The Neoproterozoic metasediments of northwestern Scotland were deformed during the 470 Ma Grampian orogeny. Their pre-Ordovician history has proved difficult to elucidate, due to conflicting evidence. While the stratigraphic record indicates deposition in intracontinental rift basins associated with the break-up of Rodinia, isotopic dates in the range 870 780 Ma from granite gneiss, early pegmatites and metamorphic garnets have been attributed to a Neoproterozoic 'Knoydartian' orogeny. Stratigraphic evidence for this orogeny is lacking, and it is not represented elsewhere on the Laurentian margin. An alternative interpretation is that much of: the Knoydartian history can be related to extensional, not collisional processes. Specifically, it has been proposed that the 870 Ma West Highland granite gneiss that is intruded into the Moine rocks of northwestern Scotland is not the product of synorogenic anatexis but represents a suite of granite sheets that were generated during extensional rifting and were subsequently deformed and gneissified during the Grampian orogeny. This contribution presents numerical models of extension-related anatexis to test this hypothesis.We first develop a methodology to estimate stretch values and the duration of extension and thermal subsidence for the Moine rift basins. A thermal model is then constructed for these basins using transient finite element techniques. This model shows that lithospheric extension sufficient to produce major rift basins, even if they are filled with feldspathic sediment with Neoproterozoic heat production characteristics, will not lead to crustal anatexis. However, a regional suite of malic dykes in the more easterly (Loch Ell) Moine suggests that stretching led to decompression melting of the mantle. We model the effect of advecting heat into the extending lithosphere by the introduction of a modest volume of basaltic magma, and show that substantial granitic melt can be generated in the basement beneath the basin. The amount of anatexis varies with the locus of basalt intrusion. Some 30% more granite is generated by dykes emplaced along basin-bounding faults than by either dykes emplaced beneath the centre of the basin, or by underplating sills. The spatial distributions of the West Highland gneiss and of the mafic suite are compatible with this finding. There is clear field evidence that the protolith of the West Highland gneiss consisted of a suite of pre-tectonic granite sheets, and our modelling demonstrates that they could have been generated during the later stages of extensional rifting and Moine sedimentation.