Abstract: A graph-constructive approach to solving systems of geometric constraints capable of efficiently handling well-constrained, overconstrained, and underconstrained configurations is presented. The geometric constraint solver works in two phases: in the analysis phase the constraint graph is analyzed nad a sequence of elementary construction steps is derived, and then in the construction phase the sequence of construction steps is actually carried out. The analysis phase of the algorithm is described in detail, its correctness is proved, and an efficient algorithm to realize it is presented. The scope of the graph analysis is then extended by utilizing semantic information in the form of angle derivations, and by extending the repertoire of the construction steps. Finally, the construction phase is briefly discussed.