This subroutine uses a variant of Sloan’s algorithm to generate an element assembly ordering that is eﬃcient when subsequently used with a frontal solver (for example, the packages MA42 and MA62). The number of ﬂoating-point operations and the storage required by a frontal solver for an unassembled ﬁnite-element matrix are dependent upon the order in which the elements are assembled; the variation in the performance of diﬀerent element orderings can be signiﬁcant. The assembly ordering obtained by MC63 is designed to reduce the maximum and root-mean-square (r.m.s.) wavefronts and the proﬁle, which in turn reduce storage requirements and computation times for the frontal solver. Only the pattern of the ﬁnite elements is used.