The large ice sheets on the northern hemisphere continents played a central role in the climate system during the Quaternary ice ages. Here we focus on the sensitivity of a three-dimensional thermodynamic ice sheet model to climatic model inputs and ice-sheet model parameters. We use the Huybrechts ice sheet model to simulate the evolution of the Northern Hemisphere ice sheets over the last glacial cycle. The time dependent forcing is constructed from UKMO Paleo-GCM time slices appropriatelyscaled with the GRIP ice core record. For a certain combination of model parametersthe ice sheet model generates a reasonable reproduction of the ice sheet extent suggested by geomorphological data and ice volume change suggested by eustatic sea level data, and we adopt this model as a useful reference model with which to compare results generated by changing ice sheet model parameters. Specific parameters examined are those related to atmospheric forcing, ice rheology, basal processes, glacial isostasy, and marine calving. Our focus is to identify the model parameters whichmost strongly control the difference in ice volume between LGM and the present day. This is achieved by exploring the axes of parameter space of the reference model and attempting to linearise the results between LGM ice volume and changes in each model parameter. Results suggest that the input climate, particularly the temperature lowering between LGM and the present day has the strongest control on LGM ice sheet volume. For the ice sheet model parameters, the linearization process shows that changes in basal sliding and variables relating to marine calving generate the most qualitatively different LGM ice sheet configurations. The hierarchy of model parameter sensitivity is presented.