In classical evidential reasoning of Shfer's model, all the sources of evidence over the same frame of discernment are underlying considered referring to the invariable decision target, and the conflicting beliefs produced by the conjunctive combination are redistributed by the combination rules to get a specific result which still lies in the same frame. Nevertheless, the sources of evidence to be combined possibly associate with different real targets in some applications, even if they are defined on the same frame. For example, in the data association in multi-target detection, the evidence from the different sensors may refer to different real-targets, although the evidence are defined in the same frame containing various targets. In such case, the fusion results should take care of the joint information of the different exclusive elements, but it is considered as conflicting beliefs in classical way. Besides, the classical frame, whose elements all refer to the single exclusive target separately, is not sufficient to represent such joint hypothesis. So the multi-dimension evidential reasoning (MDER) approach is proposed in this work. The classical frame is extended to multiple dimension denoted by M-D taking into account of the availability of the joint hypothesis of the exclusive elements called joint- element. M-D frame is composed by the joint-element, whose dimensions is coherent with the number of the independent sources. Belief functions are defined in M-D frame for decision-making. MDER is appropriate for the combination of the sources of evidence which don't necessarily arise from the same invariable decision-target. Two kinds of combination rules working in free model and constrained model are proposed for coping with different cases. Several examples are given to illustrate the use of the proposed approach and the difference between the new approach and DSmT.