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Episodic exportations of ice-rafted debris to the North Atlantic in the late Pleistocene suggest quasiperiodic ice streaming or surging activity on the northeastern margin of the Laurentide Ice Sheet. Much of this efflux of ice may originate from an ice stream issuing from Hudson Strait and tapping into core regions of the Laurentide in Hudson Bay, Labrador, and the Foxe Basin. Applying the continuum mixture theory outlined by Marshall and Clarke [this issue], we model the thermomechanical evolution of the Hudson Strait Ice Stream in a three-dimensional finite difference model of the Laurentide Ice Sheet. Our simulations focus on internal dynamics of the ice stream. Under thermal regulation of basal flow we find surge cycles of stream activity interspersed with quiescent periods where the ice stream is frozen to the bed. Modeled surge durations vary from 105 to 3260 years, while surge periodicities range from 585 to 22,410 years. With pervasively warm or cold internal temperature distributions in the ice, ice streams can also establish modes of permanent activity or inactivity under thermal regulation. Our most vigorous ice streams produce peak values of approximately 0.03 Sv of freshwater flux to the North Atlantic from basal meltwater and iceberg production. Associated ice stream velocities in this maximum case approach 6700 m yr−1. The total ice volume mobilized in a single surge event is equivalent to a global sea level rise of 0.04m in the most tranquil surge and almost 0.6m in the most extreme case. These velocities and sea level impacts axe an order of magnitude less than those predicted by MacAyeal [1993a,b], and only our most exuberant streams approach the iceberg flux estimates of Dowdeswell et al. [1995]. We propose that the sediment load of icebergs emanating from Hudson Strait in a surge event may exceed expectations from contemporary icebergs.