To solve the problem that in parametric drawing systems, unreasonable parameter values in a parametric model often result in an improper shape of a geometric object, this paper proposes a novel algebraic algorithm for determining the valid range of parameter values in certain 2-dimensional parametric drawing systems. This algorithm can solve valid range of parameters such as radius and coordinate of centre points of parametric models with only linear segments and circles. The result of the study shows that all values within the valid range provided by this algorithm can ensure that the topological shape of a geometric object does not change after reconstruction, and to some extent, this algorithm can significantly promote the efficiency of parametric drawing system design and the intel- lectual level of human-computer interaction. The analysis shows that complexity of this algorithm is O（n2）.
