PUBLISHED Polymer-clay nanocomposite (PCN) foams represent an important class of new materials in structural engineering, biomedical fields and packaging. This paper reports the relative modulus-relative density relationship, a crucial correlation in cellular solids, for low-density PCN foams. Polyurethane (PU)-natural clay nanocomposite foams with a porosity of 97% were used for studies of such relationship. The foam structures were characterised by Scanning Electron Microscopy and X-ray Micro-Computed Tomography and the modulus was obtained from compressive testing. It was found the relative modulus-relative density relationship of low-density PCN foams with porosities higher than 95% closely followed the normalised Gibson-Ashby models for open cells and closed cells, and in the case of PU-clay nanocomposite foams the geometric constant of foam C1 was determined to be approximately 0.45-0.88 in the well-established model for conventional open-cell foams, namely E f/Es = C1(?f/?s) 2 where E and ? refer to modulus and density and subscripts f and s stand for foam and solid. The effects of clay, clay content and mixing sequence on the cell structure, physical and mechanical properties of the polymer foam were also discussed The authors are grateful to the Environmental Protection Agency for supporting this work under Research Grant No. EPA 2008 PhD WRM 4. Mr Peter O?Reilly is thanked for his help with setting up the compression tests and Dr Robbie Goodhue (Geology) is thanked for facilitating access to the XRD. Ms Salma Bedair is thanked for participation in sample preparation and part of mechanical testing. The Centre for Research on Adaptive Nanostructures and Nanodevices at Trinity College Dublin is thanked for facilitating access to the Zeiss SEM