CLASSICALLY difficult nonlinear equations–those made up of polynomial expressions–can now be solved with reliability and speed. Recent advances in the mathematics of continuation methods at the General Motors Research Laboratories have practical implications for a wide range of scientific and engineering problems. The immediate application at General Motors is in mechanical design. The new method finds all eight solutions to three quadric equations in a few tenths of a second–fast enough for computer‐aided design on a moment‐to‐moment basis. Algorithms based on this method are critical to the functioning ofGMSOLID, an interactive design system which models the geometric characteristics of automotive parts.