Kineto-elastodynamics is the study of the motion of mechanisms consisting of elements which may deflect due to external loads or internal body forces. This paper describes the initial phases in the development of a general method of kineto-elastodynamic analysis and synthesis based on the flexibility approach of structural analysis, which may be applied to any planar or spatial mechanism. Dynamic error is investigated due to flexural, longitudinal, and torsional element strain, and system inertia fluctuations; the treatment of Coulomb and viscous friction is indicated. Kineto-Elastodynamic Stretch Rotation Operators are derived which will rotate and stretch both planar and spatial link vectors reflecting rigid body motion plus elastic deformations of the link. A numerical example is presented to demonstrate the elastodynamic analysis technique.