A combined finite element boundary element method for the analysis of elastoplastic stress analysis is discussed in this paper. The merged technique utilizes the Regular indirect discrete method which has been modified to enable coupling of the two methods to be achieved and maximizes the advantages of each method while minimizing their disadvantages. The merged technique is shown in particular to be useful for the analysis of elasto-plastic problems by modelling the plastic region, which normally only occupies a small area of the problem being analysed, by the finite element method and the large elastic region using the boundary element method. This approach avoids the problems associated with body diseretization in the boundary element method and the requirement for finite element models with large numbers of degrees of freedom when either of these methods are used on their own for elasto-plastic analysis. Results for the analysis of four two dimensional elasto-plastic problems are presented. These results compare well with the results from other sources and indicate that a successful union of the finite element method and the boundary element method can be achieved.