Non-Linear Resonant Decay Method (NL-RDM) addresses the identification of multi-degree of freedom non-linear systems. This method offers a practical approach to the identification of lumped parameters and continuous systems by producing a non-linear extension of the classical linear modal model. This paper is concerned with the inclusion of residual modes, below any region of interest. Any structure that is not supported to earth will have rigid body modes, being modes that have a natural frequency at zero Hertz; a good example is an aircraft. These modes are sometimes ignored but for a complete mathematical model obtained from NL-RDM the effects of rigid body modes must be analysed. NL-RDM relies on a method of curve fitting to generate modal characteristics, in terms of force, displacement, velocity and acceleration in modal space. The lower residual region was observed to contain rigid body modes. Monitoring this effect was shown to be too difficult currently for the NL-RDM, given technological restrictions. A Mass Substitution method was generated to model the system response more accurately. Its accuracy was demonstrated through case studies.