This paper is concerned with the application of model reduction methods, which are popular for linear systems, to systems with local non-linearities, modelled by using finite element analysis. In particular these methods are demonstrated by obtaining the receptance of a continuous system with cubic stiffening discrete springs using the harmonic balance method. The model reduction methods available and the choice of master coordinates are considered. In the IRS method there is a conflict in the choice of master co-ordinates between the demands in the modelling of the non-linearity and the accuracy of the linear reduction. Other reduction methods considered are the reduction to modal co-ordinates and a balanced realization approach. Reduction to modal co-ordinates is easy to apply and gives acceptable results, although a more accurate reduced model may be obtained with IRS and the best choice of master co-ordinates. Reduction based on observability and controllability considerations, via balanced realizations, gives the most accurate reduced model. The reduction methods were compared in a time domain analysis by calculating the Poincare´map of a pinned beam with clearance. The balanced realization approach gave more accurate results than the reduction to modal co-ordinates for these simulations.