Over the past 10 years, it is figured out by the firms that effective strategies are needed for increasing the competitiveness of their supply chains. Therefore, the supply chain's traditional view has been developed to sustainable supply chain perspective. Organizations that emphasize on the importance of sustainability will benefit from improved performance. For categorizing the supply chain indicators, sustainability deployment is necessary to identify the second layer or dimensions and aspects of sustainability in addition to the main sustainability dimensions such as the economic, environmental, and social dimensions. Literature has shown that in the important paradigm of sustainability, careful attention is not paid to the distinction between dimensions and aspects of sustainability. Therefore, for smoothing implementation and assessment of sustainability, consideration of the role and effect of dimensions and aspects of sustainability is essential. This paper is conducted by two fundamental and practical objectives. First, the dimensions and aspects of sustainability have been investigated and identified highlighting the lacks of conflicts in the literature. Second, the most important dimensions and aspects of sustainability are identified in one of the supply chains of Iran's oil companies using experts' opinions. The results of this research is beneficial for the researchers to consider the sustainability aspects and improve the related measures of their industries.