This paper presents efficient and accurate algorithms for the analytical detection of geometric interactions between features in a CAD environment. The developed methodology is meant to be utilized in a knowledge-based design system using feature-based modeling. The algorithms take surface information from the CAD system and use geometric inferencing to evaluate these interactions. Features represented by both convex and concave polyhedra are considered. The methodology developed here is able to deal with concave features effectively and, therefore, eliminates the need for their decomposition into convex sub-features. Sets of conditional statements based on simple and elegant rules have been developed to distinguish different types of interactions. Feature interactions are classified as intersecting or non-intersecting. For the non-intersecting cases, the features can be contained or separate and, for both cases, they can touch each other through an edge, a vertex and/or a surface. For the intersecting cases, intersections through a surface, an edge, a common edge and a common surface are identified. For all the cases the vertices, edges and surfaces involved in the interactions are identified and the relevant distances are evaluated. A computer program has been successfully implemented for polyhedral features and examples have been given to demonstrate its effectiveness.