Machine learning (ML) is widely used for building data-driven models that are highly useful for optimization. In this study, a finite element model-based adaptive ML method is presented for chip package reliability prediction and design optimization. This ML 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. The developed method was used to optimize ultra low-k chip package design. The effects of ten key design parameters on chip packaging reliability were considered. Multiple ML algorithms were evaluated for model development. It is shown that the adaptive sampling method performs much better than existing sequential sampling methods and that the finite element-based ML model can be used to achieve improved prediction accuracy for chip package design optimization.