This thesis focuses on the generation of fine cell polymer foams using a heterogeneous nucleating agent (nanoclay), appropriate polymer blending strategies and accurate control of foam processing parameters. Foaming behaviour of HMSPP/ clay nanocomposites and HMS-PP/EVA/clay nanocomposite blends is studied using a batch and a continuous foam injection moulding system. Morphological studies using TEM and SEM led to a few interesting deductions. It is very difficult to attain complete exfoliation in case of HMS-PP/clay nanocomposites even at low clay loadings due to a non polar nature and low graft efficiencies of HMS-PP matrix. The addition of clay to an immiscible blend of HMS-PP/EVA results in compatibilization between the dispersed and the continuous phase. Nanocellular foams (290 nm) were subsequently generated in the batch process at a foaming temperature of 147oC and 25 seconds foaming time. The addition of immiscible EVA-28 to the HMS-PP matrix in presence of clay particles further results in reduction of foam cell sizes to 100 nm. The effect of gas concentration, foaming temperature, injection pressure, and foaming time on foam cell size was studied. It was found that the foam cell size was highly sensitive to the injection pressure at the mould gate (hence pressure drop rate) and foaming temperature. The cell size linearly decreased with increase in gas concentration and foaming time. The sensitivity of foam cell sizes to changes in processing parameters decreases with increase in clay concentration. The effect of addition of clay particle on gas solubility was modelled using the Guggenheims contact fraction approach and subsequently a new model to predict gas solubility was developed using statistical thermodynamic tools. Additionally the effect of shear and extensional rheology on foam cell morphology was modelled. It was found that the viscoelasticity of the polymer matrix greatly affects cell sizes as compared to extensional viscosity.