Out-of-plane welding distortion has been a persistent problem in welding industries. In order to find solutions for such a problem, substantial experimental and computer modelling work on residual stresses and out-of-plane distortion analysis need to be carried out. Such computer modelling requires the temperature fields or histories during welding as pre-requisite input which can be obtained either from actual measurement or computer simulation. The object of this thesis is to develop computational techniques which can be used to compute these temperatures. Experimental work on temperature measurement has also been carried out to provide data for the purposes of validating the computer models. A data acquisition system was successfully calibrated and used to record temperature histories of the plate during the welding process. Four experiments were carried out by joining rectangular plates of size 500 min by 250 min together with "V" weld-preparation configuration at various thicknesses. Thermocouples were affixed to the top and bottom surfaces of the specimen at locations just within or very near to the heat affected zone and at locations remote from the heat affected zone to record the temperature history during welding and cooling. Related analytical theories were studied and used to validate the finite element models. The method of superposing the effects of a number of instantaneous plane heat sources to the plates has been investigated and used successfully for the evaluation of the temperature history of the plates where the heat input varies with time. Finally, a computational technique to simulate the temperature history near to and remote from the heat source was successfully developed using ANSYS 8.0 finite element software and applied to three-dimensional transient models, three-dimensional steady state models and two-dimensional transient sectional models. All the simulated results were in good agreement with experimental measurements.