The admissibility of MHD intermediate shocks has been a matter of much debate over the years. Though the legitimacy of such shocks was shown in a recent series of investigations by Wu, rigorous analytical proof of the results was considered being unsettled. In this paper, as a step towards developing such proof, we present a theory of MHD shocks. On the basis of global analysis, we develop a shock admissibility condition. Using this theory, we explain how intermediate shocks and compound waves are generated.