The natural coordinates (NCs) approach for modeling multibody systems utilizes Cartesian coordinates of points and vectors fixed on bodies, simplifying the modeling process by avoiding complexities such as Euler angles and enabling straightforward constraint equations. Nedialkov–Pryce NCs (NPNCs) are a formulation of NCs, and this article aims to showcase that NPNCs (a) are intuitive, and (b) typically give a more concise differential-algebraic equation system than do other NCs formulations when used with the Lagrangian approach. It does so by two worked examples illustrating a methodology for NPNCs.