The effect of nano-particle geometry on flow and recovery of polymer melts based on ethylene vinyl acetate (EVA) was investigated. Two nano-particles, calcium carbonate (CaCO3) and montmorillonite clay, were used with concentrations between 2.5 and 15% by weight. First, by using small amplitude oscillatory shear and transient step shear tests, the linear and non-linear response of the nano-composites was studied. Then, to examine the structure recovery, the same behavior was studied on pre-sheared samples. The linear and non-linear data revealed that the effect of nano-particles in material flow is more important for anisometric particles which can be attributed to their ability to form a fractal structure controlling the rheological properties while spherical particles are not able to form such networks. Recovery experiments revealed that while nano-composites containing spherical particles have relatively similar response in subsequent tests, the rheological properties decreased significantly for platelet particles. The recovery results were also interpreted based on a filler-network mechanism and the reduction of the nano effect for anisometric particles was related to the breakdown of the filler network. These observations were validated by morphological investigations.