This paper discusses the discourse function of the accusative case by critically reviewing the previous syntactic and semantic analyses, and then presenting the reasons why the previous analyses cannot explain the phenomenon in which the accusative case appears in the adverbial phrase. In this paper it is argued that there are two types of the accusative case: one is the structural case which is assigned to the NP with the theta role of Patient/Theme and is generated in the complement position of a verb; the other is the discourse case which is assigned to the NP which is interpreted as a patient or a theme at discourse. Moreover this paper explores discourse constraints which the adverbial phrases have to satisfy for the interpretation of a patient/theme at discourse. Firstly, if the locative argument can be interpreted as a theme, there must be the implication in which the locative arguments have to be involved in a whole area by the described action. Otherwise the action implied by a location must be performed when locomotion takes place. If the possessive argument can be interpreted as a patient, there should be interaction between the agent and the possessor in the described event. If the material argument can be interpreted as a theme, the material should remain as an indispensable part of the resulted object in the described event. Finally, if the dative argument can be interpreted as a patient, it should present with the agent at the same time and the same place to the extent that the interaction between them is implied.