A contact theory governing the discontinuous contacts between arbitrarily shaped polyhedral blocks is a major component of three-dimensional discontinuous deformation analysis method (3D-DDA). An edge-to-edge contact model

which forms a part of the contact theory

is proposed. Details are given including the detection of edge-to-edge contact type

judging of the first entrance faces

and the criteria for inter-penetration. Contact submatrices are derived by vector analysis and the penalty function method. This edge-to-edge contact model has been implemented into a 3D-DDA computer program. Two verification cases demonstrate the validity of the model and the capability of 3D-DDA to deal with large movements and multi-block interaction.