||The studies of dynamic plasticity of structures in the past 50 years mainly concerned a single structure's response to a prescribed impulsive/pulse loading or to impact of a rigid projectile. However, the collision between two deformable structures is a much more common incident in various engineering scenarios and is of practical interest. Aiming to extend our knowledge to these more realistic problems, comprehensive studies have been carried out in this thesis. A particular attention is paid to the energy partitioning between two colliding structures, which actually reveals the structure's ability to absorb energy in a collision event and is exceptionally important for developing safety devices. As the simple but representative cases, the beam-on-beam collisions are extensively studied. The rigid, perfectly plastic (R-PP) complete solutions and modal solutions are obtained. Owing to the difficulty in selecting an appropriate R-PP mode, an elastic, perfectly plastic (E-PP) modal solution is proposed to replace the R-PP modal solution. The modal solution is demonstrated to provide a good approximation to the complete solution as well as the finite element simulation. Various local contact models are proposed and implemented in the solution of beams' global deformation. Numerical results demonstrate that various local models lead to similar estimate on the global energy partitioning. The experimental study on beam-on-beam collision confirms the validity of the rigid-plastic approaches employed. Some fundamental features of structural collisions are revealed through the study of the mass-spring collision system. It is shown that the weaker structure will dissipate much more energy than the stronger one. Moreover, if the two structures do not exhibit deformation-hardening or if one structure is much stronger than the other one even with the deformation-hardening, the energy partitioning will be much less dependent on the collision velocity than the masses. These features are verified by the beam-on-beam collisions as well as a more complex ring-on-beam collision studied.