SUMMARY A technique is described wherein improved stresses can be computed in finite clement models based on displace- ment approximations. The method is based on the idea of consistent stress approximations and it approximates such stresses using the notion of a domain of influence of the stress intensity at a nodal point. Considerable improvement in accuracy of the stresses is obtained with little difficulty. The calculation of so-called 'consistent' or 'conjugate' approximations of stresses in displacement finite element formulations involves, in addition to the usual computations, the solution of an auxiliary system of linear equations, the order of which is comparable to that of the stiffness matrix itselp-<i For this reason (and despite the fact that rigorous arguments can be made that such conjugate stresses represent 'best approxi- mations' in a certain sense),5 the calculation of consistent stresses may be time consuming and expensive compared to conventional averaging methods. To overcome these shortcomings, an approximate method for computing consistent stresses in finite elements is presented in this paper. The method is also based on ideas drawn from the theory of conjugate approximations;2 it leads to smooth stress approximations in regions in which high stress gradients are experienced, and it involves only the solution of rather small systems of narrowly banded linear equations. CONSISTENT STRESSES We must first review some of the basic ideas of conjugate approximations. Consider a finite element model of an elastic body ~ which consists of a collection of E elements connected together at G nodes, and suppose that the finite element model of the displacement components ui(X) is of the form