To mitigate the disastrous effects of a blast wave, the use of layered claddings with thermal insulating materials could be a very economical solution. The present paper focuses on the study of the mechanical behaviour of a very low density insulating polyurethane foam (30 kg/m^3) under compressive loading. Static compressive tests are conducted with a press and nylon Split Hopkinson Pressure Bars (SHPB) are used to investigate the dynamic behaviour over a wide range of engineering strain rates from 10^{-5} to 10^3 s^{-1}. In addition to traditional displacement and strain measurements, the Digital Image Correlation (DIC) technique is used to observe the inhomogeneous strain fields. To better represent the mechanical state in the foam due to blast loadings, oedometric compression tests are also conducted. The foam response, showing a linear elastic stage, followed by a plastic plateau and a densification is shown to be transversely isotropic, heterogeneous and strain rate sensitive.