The definition of the solution set of a general non-linear structural probl
em depending on one external parameter is considered. Path-following techni
ques and singular point locating and identifying methods are reviewed, foll
owed by so-called branch-switching methods used to detect secondary equilib
rium paths associated with m-fold bifurcation points. Two methods introduce
d by Keller [1] and Kearfott [2] are considered, and their performance when
used together with the non-linear finite element method is verified.