This subroutine generates an ordering for ﬁnite-element matrices within a subdomain that is eﬃcient when subsequently used with a multiple front algorithm. In a multiple front algorithm, the ﬁnite-element domain is partitioned into a number of subdomains and a frontal decomposition is performed on each subdomain separately. The storage required by a multiple front algorithm and the time taken to run it are dependent upon the order in which the elements in each subdomain are input; the variation in the performance of diﬀerent element orderings can be signiﬁcant. The ordering obtained by MC53 is designed to reduce the maximum and root mean-squared wavefronts and to reduce the ﬂoating-point operation count for the frontal solver on the subdomain. The user is required to supply a list of the variables belonging to each element in the subdomain one at a time followed by a list of the variables lying on the subdomain interface using reverse communication.