The total Lagrangian finite element implementation of the Flory-Rehner free-energy function in the framework of a hyperelastic material model is addressed. It is explicitly given all the equations required to implement this material model in an implicit nonlinear finite element analysis, particularly, it is shown how to derive the so-called algorithmic or consistent linearized tangent moduli in the Lagrangian description. Some analytical and numerical results for different boundary-value problems are presented to validate the implementation.