In this paper we introduce a new technique for the real-time simulation of non-linear tissue behavior based on a model reduction technique known as proper orthogonal (POD) or Karhunen-Loève decompositions. The technique is based upon the construction of a complete model (using finite element modelling or other numerical technique, for instance, but possibly from experimental data) and the extraction and storage of the relevant information in order to construct a model with very few degrees of freedom, but that takes into account the highly non-linear response of most living tissues. We present its application to the simulation of palpation a human cornea and study the limitations and future needs of the proposed technique.