The application of dynamic relaxation, a finite difference based iterative analysis, to the study of plates to date is reviewed. The extension of the method to include both geometrical and material non-linear effects in plates is then described in detail. Particular attention is paid to aspects of the iteration parameters which control convergence. The advantages of interlacing finite difference meshes is discussed and the mesh refinement necessary for the accurate analysis of plates in compression and in shear is considered. The usual elastic out-of-plane boundary conditions are generalised by the inclusion of terms applicable in the elasto-plastic range, and the role of in-plane boundary restraints is discussed in respect of plating in both bridge and ship structures. The scope of the method is demonstrated by examples of a long plate with patch loading normal to the undeflected plane of the plate and a panel of a box girder web. In both cases, the effects of initial out-of-plane geometric distortions and welding residual strains on behaviour up to and beyond collapse are considered.