In this talk I will briefly introduce the mixed finite element method and show their applications. I consider Poisson, elasticity, Stokes and biharmonic equations for the applications of the mixed finite element method. The mixed finite element method also arises naturally in Stokes flow, multi-physics problems as well as when we consider non-conforming discretisation techniques. I will also present my recent works on the mixed finite element method for biharmonic and Reissner-Mindlin plate equations.