The evolution of past permafrost since the Last Glacial Maximum (LGM) is simulated using the Vrije Universiteit Amsterdam Permafrost (VAMPER) model. This method is different from a proxy-based approach which translates reconstructed air temperatures to estimate past permafrost extent and thickness. First, a sensitivity analysis was performed to assess the behaviour of the model. Then five case studies within Eurasia were performed using mean annual ground surface temperatures derived from an Earth system model as the surface forcing. In Central and West Siberia, the simulated LGM permafrost thicknesses of 730-940m and 365-445m, respectively, agree well with previous estimates. The LGM and present-day estimates for South Russia (9-15m) are underestimated, which is likely due to a highly simplified land-atmosphere coupling. In West and Central Europe, however, the VAMPER model was not able to produce permafrost during LGM conditions, which is due to previously recognised biases of the Earth system model. A supplementary simulation was then performed, resulting in an LGM permafrost thickness estimate of 260-320m. Average thawing rates are on the order of 1 to 3cm/yr except for Central Siberia, where permafrost thawed at rates of 0.3 to 0.4cm/yr. Overall results of these simulations provide a basis for future improvement in modelling the permafrost-climate relationship over millennia. © 2013 John Wiley & Sons, Ltd.