Hoppe (1965) provided a fundamentally different model of ice flow. In eastern Shetland many of Peach and Horne’s interpretations of ice flow directions, based on striae and ice-moulding observations, were reversed. The resultant model showed a dominantly radial flow from a local ice cap. Older sets of striae were noted, for example on Bressay which showed movement from the north-east and possibly suggested Scandinavian glaciation. Hoppe maintained that Shetland had been originally glaciated by Scandinavian ice and that the local icecap was a climatically inactive remnant of this ice sheet. Most of the observed striae were formed during a two-phase deglacial process: rapid open-water ice calving associated with the retreat of Scandinavian ice, and melting of the local ice cap. Diverging striae, such as those on North Roe and Walls, or striae that did not conform to the regional pattern, such as at Esha Ness, were accommodated by the shift between these two phases of deglaciation.

Mykura (1976) provided additional information for radial flow from an ice cap over central Shetland. To account for westward carry of erratics on Unst, Mykura suggested that Scandinavian ice lay just east of Shetland and either flowed across the area directly or diverted the flow Shetland ice to recurve to the north and west. Westward erratic carry in southern Mainland was attributed directly to Scandinavian ice. The resultant ice flow lines look unrealistic for a single phase of ice floe in northern Shetland. Mykura added further evidence for fluctuating directions of ice flow in many parts of Shetland but he considered that retreat to Scandinavian ice allowed climatically active expansion of the local ice cap. He noted that there were clear signs of eastward flowing ice in southern Mainland, where there was also evidence of earlier westward carry. Mykura was not able to determine however if this later expansion of local ice covered Unst and Yell.

Flinn in a sequence of papers has provided important observations of the local glacial record on islands from Foula to Fair Isle and extended his investigations offshore to explore the evidence on the bed of the North Sea. Flinn (1983) identified an ice shed stretching almost the length of the islands from a local ice cap which did not cover the northern tip of Unst. His former arguments in favour Scandinavian ice offshore at this time were rejected, and divergent ice flow patterns on Shetland were seen instead as a result of the influence of seabed topography. With evidence from the northern North Sea that Scandinavian ice did not cross the Norwegian trench in the Late Devensian, Flinn concluded that any glaciation of Shetland by Scandinavian ice must have predated the last glaciation. The presence of meltwater channels, glaciofluvial sands and gravels, a proglacial lake and periglacial slope deposits in North Unst and Yell might be relate to deglaciation, but Flinn suggested that the absence of till and striae in these areas is indicative of an ice margin just to the north. Long and Skinner (1985) provided some support for Flinn's ice limit on Unst from till distribution on the adjacent seabed. Consideration however of the equivalent drift limit which seems to extend 75 kilometres east of Shetland produces an implausible ice sheet configuration.

Ross (1996) reviewed existing data and added new observations from offshore to provide a model of fluctuating ice margins during the Late Devensian. Off eastern Shetland, the ice margin at the glacial maximum is indicated by the limit of brown glacial deposits sourced from Shetland and lay around 100 km SE of Out Skerries (Peacock, 1995). To the west ice reached the continental shelf. As the ice margin retreated, the ice shed shifted, creating complex patterns of ice flow as the underlying topography began to exert a progressively greater influence on ice flow.

The ice margins east and west of Shetland demonstrate that the last ice cap was large, around 150 km across. The ice shed shifted over time but its average position is indicated as resting over the spine of the islands, as envisaged by Flinn, and corresponds with a zone of relatively limited erosion with restricted signs of ice roughening. The manner in which metamorphic erratics extend high on Ronas Hill requires not only that the ice shed lay to the east but it was significantly higher than this summit (450 m), as ice had to be driven uphill. Foula has ice moulding and erratics extending to at least 200m and there is no sign that the hills stood as nunataks above the last ice sheet (Flinn, 1978). Adopting the 'fried egg' shape of the ice sheet profile from northern Scotland (Ballantyne  et al, 1998), with steep ice surface slopes over the rigid hard rock beds on Shetland and gentler surface slopes on the soft, deformable beds of the North Sea and North Atlantic, implies that the ice surface stood at around 500-800 m in the ice shed zone over central Shetland.

Research work on the glaciation of Shetland is set to accelerate as the importance of understanding the glacial history of the islands is recognised for reconstructions of ice sheet dynamics in the Norwegian Channel, north North Sea and the West Shetland Platform. The latest models of the Scottish ice sheet developed by Hubbard in Edinburgh show a thin, cold-based ice mass over Shetland, a picture that is at odds with the widespread evidence of glacial erosion across the islands. Perhaps Shetland received more snowfall? Davison and Stoker at BGS Edinburgh are working across the sea bed from St Magnus Bed to the shelf edge, identifying a series of moraine ridges related to the maximum limit and decay of the last ice cap on Shetland.