An investigation into the parametric and non-parametric modelling of a two dimensional flexible plate structure is presented in this paper. The parametric approaches obtaining linear parametric models of the system using recursive least squares and genetic algorithms. The non-parametric models of the system are developed using a non-linear AutoRegressive process with eXogeneous input model with multi-layered perceptron neural networks, Elman recurrent neural networks and adaptive neuro-fuzzy inference systems. The models are validated using several validation tests including input-output mapping, mean squares of error and correlation tests. A comparative assessment of the techniques used is presented and discussed in terms of accuracy, efficiency and performance in estimating the modes of vibration of the system.