Composite beams using bolts to attach steel plates to the side faces of existing reinforced concrete (RC) coupling beams can enhance both their strength and deformability. The behavior of those composite beams differs substantially from the behavior of typical composite beams made up of steel beams and concrete slabs. The former are subjected to longitudinal, vertical and rotational slips, while the latter only involve longitudinal slip. In this study, a mixed analysis method was adopted to develop the fundamental equations for accurate prediction of the load-carrying capacity of steel plate strengthened RC coupling beams. Then, a rigid plastic analysis technique was used to cope with the full composite effect of the bolt group connections. Two theoretical models for the determination of the strength of medium-length plate strengthened coupling beams based on mixed analysis and rigid plastic methods are presented. The strength of the strengthened coupling beams is derived. The vertical and longitudinal slips of the steel plates and the shear strength of the anchor-bolt connection group is considered. The theoretical models are validated by the available experimental results presented in a companion paper. The strength of the specimens predicted from the mixed analysis model is found to be in good agreement with that from the experimental results.