In this article, the dependence of tortuosity on the geometrical structure of a porous medium is studied. In particular, the considered porous media have anisotropic structures, being composed by a collection of object of similar shape, with a well-defined orientation. Geometrical expressions for the tortuosity as a function of the porosity, of shape factors characterizing the geometry of the solid objects and of the orientation of the flow with respect to the object axes are derived. Besides the general case, two simpler expressions are derived for 2D porous media and for media composed by axisymmetric objects. The expressions for the two particular cases are validated through a series of numerical simulations of diffusion phenomena, finding a good agreement. The model is also compared with experimental data from literature, showing its possible use in the prediction of the transport properties of a porous medium made by assembling similar solid particles, by a simple geometrical characterization of its components. Finally, a parametric analysis is performed, showing a strong dependence of the tortuosity on the objects shape and on their orientation with respect to the flow. The capability of the presented model to predict such effects can be used to design materials with particular non-isotropic transport characteristics.