Nanoparticles (NPs) are used for drug delivery with enhanced selectivity and reduced side-effect toxicity in cancer treatments. Based on the literature, the influence of the NPs mechanical and geometrical properties on their cellular uptake has been studied through experimental investigations. However, due to the difficulty to vary the parameters independently in such a complex system, it remains hard to efficiently conclude on the influence of each one of them on the cellular internalization of a NP. In this context, different mechanical / mathematical models for the cellular uptake of NPs have been developed. In this paper, we numerically investigate the influence of the NP's aspect ratio, the membrane tension and the cell-NP adhesion on the uptake of the NP using the model introduced in 1 coupled with a numerical stochastic scheme to measure the weight of each one of the aforementioned parameters. The results reveal that the aspect ratio of the particle is the most influential parameter on the wrapping of the particle by the cell membrane. Then the adhesion contributes twice as much as the membrane tension. Our numerical results match the previous experimental observations.