The use of Finite Element (FE) based homogenisation has improved the study of composite material properties. A homogenisation is a method of averaging a heterogeneous domain by using a replacement unit cell according to the proportions of constituents in the domain. However, the homogenisation method involves enormous computational effort when implemented in engineering design problems, such as optimisation of a sandwich panel. The large number of computations involved can rule out many approaches due to the expense of carrying out many runs. One way of circumnavigating this problem is to replace the true system by an approximate surrogate model, which is fast-running compared to the original. In traditional approaches using response surfaces, a simple least-squares multinomial model is often adopted. In this thesis, a Genetic Programming model was developed to extend the class of possible models by carrying out a general symbolic regression. The approach is demonstrated on both univariate and multivariate problems with both computational and experimental data. Its performances were compared with Neural Networks - Multi-Layer Perceptrons (MLP) and polynomials. The material system studied here was the auxetic materials. The auxetic behaviour means that the structure exhibits a negative Poisson's ratio during extension. A novel auxetic structure, chiral honeycomb, is introduced in this work, with its experiments, analytical and simulations. The implementations of the auxetic material surrogate models were demonstrated using optimisation problems. One of the optimisation problems was the shape optimisation of the auxetic sandwich using Differential Evolution. The shape optimisation gives the optimal geometry of honeycomb based on the desired mechanical properties specified by the user. The thesis has shown a good performance of numerical homogenisation technique and the robustness of the GP models. A detailed study of the chiral honeycomb has also given insight to the potential application of the auxetic materials.