A model of the growth and decay of the Antarctic Peninsula Ice Sheet during the last glacial/interglacial cycle is used to identify the main controls on ice sheet behavior. Using as input glaciological assumptions derived by W. F. Budd and I. N. Smith (1982, Annals of Glaciology 3, 42–49), bedrock topography, isostatic compensation, and mass balance relationships, the model is driven by sea-level change over the last 40,000 yr in association with assumed changes in the rate of melting beneath ice shelves. An ice sheet dome over 3.5 km thick grows on the offshore shelf and straits west of the Antarctic Peninsula and reaches a maximum at 18,000 yr B.P. Collapse begins at 14,000 yr B.P. but becomes rapid and continuous after 10,000 yr B.P. The present stable ice cover is achieved at 6500 yr B.P. Ice growth and decay are characterized by thresholds which separate periods of steady state from periods of rapid transition; the thresholds usually relate to topography. Tests show that ice sheet behavior is most sensitive to sea-level change, basal marine melting, and accumulation and is less sensitive to isostasy, spatial variation in accumulation, calving rates, and ice flow parameterization. Tests of the model against field evidence show good agreement in places, as well as discrepancies which require further work.