This paper presents several algorithms to detect the cable interferences for a general spatial Cable-Driven Parallel Robot (CDPR). Two types of cable interferences are considered. The first type is the collisions between cables and cables. The second type is the interferences between cables and the CDPR mobile platform. In each case, an algorithm is proposed to efficiently verify the cable interferences. The use of the proposed algorithms is then illustrated by a verification procedure of the collision free condition over a given Cartesian workspace and orientation workspace of a CDPR. These tools can be used in the design or planning phase of a general CDPR.