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Several factors had led to increase competition among companies and then transferring this competition to supply chain. While the competition is getting more intense, the quick response to demand changing becomes increasingly important and agility will be a key strategy for the survival and persistence in competitive market. The concept of agile supply chain had developed as a means of achieving the capability of quick responding to demand changing in challenging competitive environment. The Success of operation in an agile supply chain relies heavily on choosing the most suitable partner in any condition. The aim of this research is to identify partner selection criteria and represent the relations between them. For these purposes we have used a tree-stage model. In the first stage, we extracted the criteria from literatures. Second stage was done to reduce the criteria to a lower number by interviewing with top managers of the company and using Fuzzy screening method. In the last stage interpretive structural modeling was used to identify the relationships between criteria and MICMAC analysis was used to classify them. After data analysis, variables were categorized in eight levels and then the ISM digraph was plotted. After the MICMAC analysis was done, the criteria was classified to independent, dependent and linkage variable and no criteria were identified as autonomous variables. Determination of the relationships between variables and types of variables can lead to a better perception of the issue and make appropriate decisions in the selection of partners. [ABSTRACT FROM AUTHOR]