The goal of the Palaeoclimate Modelling Intercomparison Project (PMIP) is to understand the response of the climate system to changes in different climate forcings and to feedbacks. Through comparison with observations of the environmental impacts of these climate changes, or with climate reconstructions based on physical, chemical or biological records, PMIP also addresses the issue of how well state-of-the-art models simulate climate changes. Palaeoclimate states are radically different from those of the recent past documented by the instrumental record and thus provide an out-of-sample test of the models used for future climate projections and a way to assess whether they have the correct sensitivity to forcings and feedbacks. Five distinctly different periods have been selected as focus for the core palaeoclimate experiments that are designed to contribute to the objectives of the sixth phase of the Coupled Model Intercomparison Project (CMIP6). This manuscript describes the motivation for the choice of these periods and the design of the numerical experiments, with a focus upon their novel features compared to the experiments performed in previous phases of PMIP and CMIP as well as the benefits of common analyses of the models across multiple climate states. It also describes the information needed to document each experiment and the model outputs required for analysis and benchmarking.