We discuss the implementation and performance of several Newton-like solution algorithms, for large-scale elasto-plasticity finite element analyses. The iterative schemes used are: Truncated Newton, Quasi-Newton, limited storage QN and element-by-element QN. Among the aspects examined are: the effect of inexact computation in the Truncated Newton algorithm, the influence of the line search accuracy and the overwriting strategy employed and number of updates stored in the limited storage QN methods. It is shown that the element-by-element QN method is particularly efficient and has a number of important advantages.