The tortuosity is one of the key parameters to characterize the transport properties of porous media. Since the tortuosity is strongly related with the shape of particles constituting the porous media, we need to investigate the shape effect of particles on the tortuosities. We have, respectively, performed a series of finite element simulations for the hydraulic and the electric tortuosity to reveal the relationship between the tortuosity and the particle shape. The results reveal that: (1) A concise computational expression for tortuosities proposed by Duda et al. is numerically validated through our simulations. (2) On average, the hydraulic tortuosity is 15 % greater than the electric tortuosity within the porosity range from 0.5 to 0.9. (3) The high particle aspect ratio (5.0) results in the amplifications of both the hydraulic and the electric tortuosities up to 15 % greater than the values with the low particle aspect ratio (1.0). Using the simulation results, we propose a novel tortuosity model based on the van Genuchten-type function, which can precisely describe the relationship between the tortuosities and the porosity for elliptic particle having the aspect ratio ranging from 1.0 to 5.0.