Purpose Today, with the increasing involvement of the environment and human beings business units, paying attention to fulfilling social responsibility obligations while making a profit has become increasingly necessary for achieving sustainable development goals. Attention to profit by organizations should not be without regard to their social and environmental performance. Social responsibility accounting (SRA) is an approach that can pay more attention to the social and environmental performance of companies, but it has many barriers. Therefore, the purpose of this study is to identify barriers to SRA implementation and provide strategies to overcome these barriers. Design/methodology/approach In this study, the authors identify barriers to social responsibility accounting implementation and provide strategies to overcome these barriers. By literature review, 12 barriers and seven strategies were identified and approved using the opinions of six academic experts. Interpretive structural modeling (ISM) has been used to identify significant barriers and find textual relationships between them. The fuzzy technique for order performance by similarity to ideal solution (TOPSIS) method has been used to identify and rank strategies for overcoming these barriers. This study was undertaken in Iran (an emerging market). The data has been gathered from 18 experts selected using purposive sampling and included CEOs of the organization, senior accountants and active researchers well familiar with the field of social responsibility accounting. Findings Based on the results of this study, the cultural differences barrier was introduced as the primary and underlying barrier of the social responsibility accounting barriers model. At the next level, barriers such as “lack of public awareness of the importance of social responsibility accounting, lack of social responsibility accounting implementation regulations and organization size” are significant barriers to social responsibility accounting implementation. Removing these barriers will help remove other barriers in this direction. In addition, the results of the TOPSIS method showed that “mandatory regulations, the introduction of guidelines and social responsibility accounting standards,” “regulatory developments and government incentive schemes to implement social responsibility accounting,” as well as “increasing public awareness of the benefits of social responsibility accounting” are some of the essential social responsibility accounting implementation strategies. Practical implications The findings of the study have implications for both professional accounting bodies for developing the necessary standards and for policymakers for adopting policies that facilitate the implementation of social responsibility accounting to achieve sustainability. Social implications This paper creates a new perspective on the practical implementation of social responsibility accounting, closely related to improving environmental performance and increasing social welfare through improving sustainability. Originality/value Experts believe that the strategies mentioned above will be very effective and helpful in removing the barriers of the lower level of the model. To the best of the authors’ knowledge, for the first time, this study develops a model of social responsibility accounting barriers and ranks the most critical implementation strategies.