This book clearly describes about prediction of breakdown voltage of solid insulator due to voids. The voids or cavities within the solid insulating material during manufacturing are potential sources of electrical trees which can lead to continuous degradation and breakdown of insulating material due to Partial Discharge (PD). A major field of Artificial Neural Networks (ANN) and Least Square Support Vector Machine (LS-SVM)application is function estimation due to its useful properties, such as, non-linearity and adaptively particularly when the equation describing the function is unknown. Here this book shows about the breakdown voltage due to PD in cavities for five insulating materials under AC conditions has been predicted as a function of different input parameters, such as, the thickness of the insulating sample, the thickness of the void, diameter of the void, and relative permittivity of materials or by using two different models. On completion of training, it is found that the ANN and LS-SVM models are capable of predicting the breakdown voltage very efficiently and with a small value of Mean Absolute Error.