A numerical technique is presented for analysing diffraction gratings of arbitrary groove shape. The method is based on the application of finite element technique. It is suggested that this technique, thus far reserved mostly for the problems of bounded extent, may be used to advantage for analysing this problem. To this end, the infinite space is divided into two regions, one finite and the other infinite in extent. A series solution is employed in the infinite region, and in the finite one a functional is used. The two solutions are then matched on the common boundary of the two regions. The resulting equation for the field is finally solved by application of the finite element technique. The numerical results obtained for echelette gratings are favourably compared with a number of similar results reported in the literature.