Description of the interactions between rigid bodies with a particular emphasis on constraint forces. The resultant torsor (resultant force-moment) associated to a system of forces is defined. Interaction torsors associated with the usual interactions in mechanical systems (gravitational attraction, tosion springs, and dampers) are formulated. The chapter proposes an original and rigorous treatment of constraint links with total and tangent redundancy, yielding indeterminacy and ill-conditioning in the mechanical constraints design. The analytical characterization of constraint torsors is proved and applied to different examples. Finally, the limit conditions leading to constraint partial or total loss (contact loss, overturning, sliding, rolling, pivoting) are explored.