Three main failure mechanisms of ULSI interconnects are the electromigration (EM), stress induced voiding (SIV) and low-k dielectric breakdown. Reliability tests for these mechanisms are too long to meet the development time requirement, and the underlying dominant mechanisms cannot be identified, rendering difficulty in design-in reliability for integrated circuit. Facing the challenges in the reliability study of the interconnect system, physics based simulation and modeling is found to be essential, and finite element method (FEM) is a suitable tool. A few examples on the application of FEM to study the degradation processes and identification of potential failure sites in interconnects due to EM and SIV are given here. The study of the process induced degradation of the effective k value of low-k dielectric in ULSI interconnect system using FEM is also presented.