Welding has been one of the most extensively used joining processes for engineering applications and is the most frequently used process in nuclear power plants. Welding involves complex thermal, mechanical and metallurgical phenomena, affecting the microstructure of the material and generating internal or residual stresses and distortions in the process. Residual stresses are locked up stresses resulting from the thermal and/or mechanical processing of the parts. Residual stresses are inevitable and usually detrimental to the service life of a component often resulting in collapse or total structure failure. Numerous welding techniques have been developed over the past decades with the aim to reduce the residual stresses and enhance the performance of the component. These techniques need to be thoroughly studied and understood before implementing them in actual service. Electron beam welding and laser beam welding are two emerging techniques that are most promising because of many favourable features, including narrow fusion width to depth ratio, high welding speeds and capability to join metals that are dissimilar without any filler material. However to understand the full capability of these methods, it is essential to study the processes and their consequences on the joint. This dissertation presents the development of numerical and experimental approach to analyse electron beam welding and laser beam welding in a modified 9Cr-lMo (P91) butt welded plate. Modified 9Cr-lMo steel is used in nuclear power plants because of its high desirable properties such as strength and creep resistance at high temperatures. A number of simulation procedures using sequentially coupled thermo-mechanical analysis of the welding process are developed to study the welding process and the generation of residual stresses. The model incorporates the sol id-state phase transformation, exhibited by P9l steel during rapid cooling stage, which is the critical factor in the final residual stress field. The finite element models are validated using neutron diffraction measurements. The validated models are then used to study the influence of material properties, hardening models, annealing temperature and the boundary conditions on the final residual stress distribution . Also post-weld heat treatment used for relaxing the residual stresses due to welding is simulated and the extent of relaxation is studied. Uniaxial cross-weld creep tests are conducted on electron-beam welded samples to investigate the creep life. With the experience gained from modelling electron beam welding on P91 plates, an attempt has been made to develop a finite element model to simulate the electron beam welding of dissimilar metal welds in a butt plate made of P91 and AISI 316LN SS steels. The developed model is evaluated based on neutron diffraction experiments. Significant amount of effort has been directed towards developing an accurate and reliable numerical model to simulate the complex phenomena and severe non-linearity associated with welding processes such as temperature dependent material properties, hardening models, boundary conditions and solid-state phase transformation, which is the main purpose of this research. The residual stresses are predicted successfully. It is shown that the major contributor towards the residual stress profile is the volume change associated with the solid-state phase transformation during the cooling stage. Other factors such as temperature dependent thermo-mechanical properties, material hardening properties and boundary conditions have relatively less influence on the residual stresses.