The development of the finite element method for the numerical analysis of the mechanical behaviour of structures has been directed at the calculation of the state of deformation and stress of kinematically determinate structures. The discretized description of the kinematics of kinematically indeterminate structures as given in the finite element method is however also a good starting point for the numerical treatment of the analysis of mechanisms. In the description of the kinematics of mechanisms the relations between deformations and displacements play a central role. For the calculation of the transfer functions of order one and two, being the basic information for the determination of velocity and acceleration, direct methods are presented, applicable to mechanisms consisting of undeformable links. The description is completed with the formulation of dynamics, kinetostatics and vibrations. For mechanisms consisting of deformable links an approximate method is given. The theory is applied to planar mechanisms. Examples demonstrate the use of the theory in kinematic, dynamic and kinetostatic problems.