This article is the first of two parts in which algorithms are presented concerning the contact detection between two cylinders, and a cylinder and a flat surface. This first part presents the equations for contact detection, contact location, contact overlap, and normal contact direction. The second part focuses on validation of the algorithm. These articles are the first to present validated algorithms and relations for all potential cylinder-plane and cylinder-cylinder contact scenarios (ten in all). (C) 2010 Elsevier Ltd. All rights reserved.