The Stefan-Maxwell equations form a system of nonlinear partial differential equations (PDE), that describe the diffusion of multiple reacting or non-reacting species in a container. These equations are of particular interest for their applications to biology and chemical engineering. The Stefan-Maxwell equations provide the fluxes of all species in an implicit way as a function of the gradient of partial pressures. The diffusion coefficients depend on the partial fractions of the species,this leads to a system of coupled nonlinear PDEs. In the engineering literature this system is inverted to express each flux as a combination of the gradient of partial fractions before any numerical method is applied. In our talk, we show that the Stefan-Maxwell equations naturally lead to a mixed variational formulation, making the inversion of the system unnecessary before the application of the finite element method. The use of such formalism has not been proposed so far in the literature on Stefan-Maxwell equations. We then show that the nonlinearity can be dealt with through a linearization and conditions for the well posedness of the linearized formulation can be determined. Next, the variational formulation is approximated using mixed finite element methods, in particular with Raviart-Thomas elements. A priori error estimates for the mixed finite elements can be extended to the linearized Stefan-Maxwell equations. Numerical results are presented showing the accuracy of the method with order of convergence matching the error estimates.