Singularity analysis is an important subject of the geometric constraint salisfaction problem. In this paper, three kinds of singularites are described and corresponding identification methods are presented for both under-constrained systems and over-constrained systems. Another special but common singularity for nuder-constrained geometric systems, pseudo-singularity, is analyzed. Pseudo-dingularity is caused by a variety of constraint match-ing of under-constrained systems and can be removed by improving constraint distribution. To avoid pscudo-singularity and decidc redundant constraints adaptively, a differentatin algo-rithm is proposcd in the papar. Its correctncss and efficicncy have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.