We describe an algorithm for determining the interference or penetration distance between two moving objects. The objects are assumed to be specified by quadratic and/or linear constraints and thus, encompass a wide variety of objects encountered in robotics and multibody dynamics applications. The interference distance problem is formulated as a constrained optimization problem where we maximize the shrinkage of both objects, while maintaining a non-empty intersection volume between them. The key to the present algorithm is a nonlinear transformation which allows a closed-form description of the shrunk bodies. The resultant nonlinear programming problem is solved using an existing optimization scheme which is based on a recursive quadratic programming technique. The paper concludes with a numerical example demonstrating the validity and the computational efficiency of the proposed solution.