A finite element method of the perturbed mixed type for rubber elasticity applications is presented. The method is novel in the sense that the perturbation parameter appearing in this method is not artificial but can be identified with the measurable bulk modulus of a nearly incompressible material. The usage of elements with local pressure variables makes the method equivalent to a penalty method of the projection penalty type. An updated Langrangian formulation of the method is presented. The application of the method to some simple engineering problems is demonstrated.