Creep deformation in welded pipes and plates is of particular importance in the power industries. Most failures of welded pipes occur in the type IV region at the boundary with the parent material, which is relatively much harder. This thesis extends the work of Nicol (1985), Hawkes (1989) and Newman (1993) on the Cosserat theory of plates and shells, and has two major aims. The first is to develop the work of Hawkes to model successfully the strain rates in four-zone, thickwalled welded pipes. It is possible to determine the effects that the thickness of the pipe wall, the radius of the pipe and the creep index, n, in Norton's law have on the strain-rate distribution throughout the pipe. Using Continuum Damage Mechanics and this Cosserat model, the position and time to rupture in welded pipes is then calculated. The second aim of this thesis is to develop further the initial modelling work of Nicol (1985) and Hawkes (1989) by obtaining some simple perturbation models for both welded pipes and plates. The results obtained with the perturbation solutions are then compared with the numerical solutions of Newman (1993) for a plate and the numerical solutions derived in this thesis for a pipe.