We use a two-dimensional, full-stress, thermomechanical flow band model to investigate late Pleistocene and Holocene histories of ice thickness and ice flow at Siple Dome in West Antarctica. Measurements obtained from an ice core and borehole near the ice divide and measurements of radar-detected internal stratigraphy are used as targets for modeling. Models that account for the climate history (accumulation rate and temperature) alone yield a poor match to observations; histories of ice dynamics (ice thickness, ice divide location, and ice flow enhancement) also need to be included. Our favored model includes 350 m of thinning at Siple Dome between 15,000 and 14,000 years ago, onset of divide flow 3000 years ago, ongoing divide migration starting 2500 years ago, and evolution of ice fabric over the past 30,000 years. The timing of thinning is earlier than that inferred from geologic evidence from the margins but is coincident with a 20 m rise in global sea level about 14,500 years ago (meltwater pulse 1A). This opens the possibility that thinning was a result of increased activity of the ice streams in the late Pleistocene, forced by meltwater pulse 1A. The contribution to meltwater pulse 1A as a result of this thinning was likely small.