Flexible polyurethane/clay porous nanocomposite foams were synthesized using natural and organically modified montmorillonite clays such as bentonite, closite 10A and closite 30B. The content of nanoclays was varied from 1 to 5 wt% of polyol. Dispersion of clay in Polyurethane(PU) matrix was investigated by X-ray diffraction(Cu-$K{alpha}$ rays of wavelength $1.54{AA}$) using an X-ray diffractometer. Also, we determined that the thermal resistance of PU foam increased with added clay, compared to that of pure PU foam. The cell size and the fraction of open cells of the precursor foam were controlled by the addition of clay to the polyurethane foam. Modified clays were found to be more efficient cell openers than the unmodified clay. In addition, the tensile strength and elongation of the polyurethane/clay porous nanocomposites were examined. Increasing clay content increased the mechanical properties of the composites, such as tensile strength, and elongation at break. However, increasing the content over 5 wt% deteriorated the properties of the composites. We found that the nanofillers(bentonite, closite 10A and closite 30B) improved the thermal stability of the nanocomposite foam. The nanocomposite foam containing 3 wt% of closite 30B exhibited the best tensile strength and thermal stability.