Chip-package interaction (CPI) is important for the reliability of advanced Cu/low k chips incorporating low-k (LK) and extreme low-k (ELK) dielectrics. Wiring density of advanced low-k Cu chips is quantified and its effects on the Chip Package Interaction are investigated by a multi-level finite element analysis (FEA). The CPI of mixed signal chip and very-large-contact-density package is studied. In addition, an energy release rate (ERR) ratio was defined and found to be a proper criterion to evaluate the CPI reliability. The effects of wiring density were attributed to the Dundurs effect due to the material mismatch and the nonuniform metal density in the mixed-signal and very-large-contact-density packages. In a study of the pillar structure effect, intermetallic compound (IMC) growth, bump shape and orientation were found to be important and could substantially impact the ERR ratio. A finite element model-based adaptive machine learning method is developed for chip package reliability prediction and design optimization to improve the computational efficiency. This machine learning method employs a validated multi-scale finite element model for training data generation. An adaptive sampling scheme is developed to optimize the training process with a steepest descent algorithm. Multiple machine learning algorithms were evaluated for model development. A significant improvement on prediction accuracy was achieved by the developed adaptive sampling and machine learning scheme, and the developed model was successfully applied to optimizing an ultra low-k chip package design.