Strain technology has been successfully integrated into CMOS fabrication to improve carrier transport properties since 90nm node. Due to the non-uniform stress distribution in the channel, the enhancement in carrier mobility, velocity, and threshold voltage shift strongly depend on circuit layout, leading to systematic performance variations among transistors. A compact stress model that physically captures this behavior is essential to bridge the process technology with design optimization. In this paper, starting from the first principle, a new layout-dependent stress model is proposed as a function of layout, temperature, and other device parameters. Furthermore, a method of layout decomposition is developed to partition the layout into a set of simple patterns for efficient model extraction. These solutions significantly reduce the complexity in stress modeling and simulation. They are comprehensively validated by TCAD simulation and published Si-data, including the state-of-the-art strain technologies and the STI stress effect. By embedding them into circuit analysis, the interaction between layout and circuit performance is well benchmarked at 45nm node.