The thermal couplings among capacitors in a bank could significantly alter the reliability performance compared to a single capacitor. The impact of thermal coupling is becoming stronger for high power density systems due to more stringent constraint in volume. Prior-art studies take into account the thermal coupling effects of a capacitor bank by either Finite Element Method (FEM) or experimental characterization, which are case dependent and time-consuming. This paper proposes a nonlinear mathematical model for capacitor banks based on physics of thermal conduction, convection, and radiation. A simplified version of the model is also obtained and represented by an RC circuit network, which enables computational-efficient thermal stress modeling. The proposed models are convenient to use to support model based sizing of capacitor banks and is scalable for multi-cell rectangle layout. A case study with experimental testing is discussed to verify the accuracy of the models.