Use of constraint-based techniques in interactive graphics applications poses a variety of unique challenges to system implementors. This paper begins by describing how interface concerns create demands on interactive, constraint-based, graphical applications. We will discuss why such applications must be able to handle systems of non-linear constraints, and survey some of the techniques available to solve them. Employing these numerical algorithms in the contexts of interactive systems provides a set of challenges, including dynamically setting up the equations to be solved and achieving adequate performance and scalability. This paper will explore these issues and describe the methods we have used in our efforts to address them.