The objective of this research is to develop a design framework for virtual prototyping of electronic packaging. This framework couples computational mechanics and fluid dynamics, based on finite volume method with integrated finite element routines, with numerical optimisation and statistical methods. This integrated approach is intended as a modelling tool for calculating optimal design solutions for electronic packaging and component assembly with a focus on die reliability and the thermal management. The motivation is to introduce numerical optimisation theory as an approach for a fast, systematic and automated design approach for wide range microelectronics applications. The proposed methodology will also benefit from multi-physics numerical analysis to predict complex behaviour of electronic packages, systems and processes subject to different operational or environmental conditions. This thesis demonstrates multi-physics modelling (i.e. integrated solutions for fluid flow, heat transfer and stress) coupled with gradient/non-gradient based numerical optimisation techniques and associated statistical methods. An explanation and comparison of the two approaches to numerical optimisation — (1) Response Surface Methodology (RSM) based on Design of Experiments (DoE) and (2) direct gradient based and non-gradient methods - are given. Both the advantages and limitations of these virtual design strategies, with respect to their integration with multi-physics modelling, are discussed and demonstrated. This integrated multiphysics/optimisation design approach is demonstrated on a variety of problems from the area of microelectronics design and packaging. The thesis demonstrates this for three industrial examples. These are: The software packages used to develop the design tool and to undertake the outlined studies are PHYSICA and VisualDOC. PHYSICA is a multiphysics finite volume based simulation tool with integrated modules for finite element solid mechanics analysis. The software framework is detailed in Chapter 2, Section 2.4 and further in Chapter 4. The VisualDOC tool offers a collection of numerical optimisation routines and modules for statistical analysis (Design of Experiments) and approximate Response Surface modelling. VisualDOC framework is discussed in Chapter 4, Section 4.8.