Corporate sustainability is an intensely analyzed concept in the literature worldwide, in terms of social, environmental and economic impact. The applicability of the concept on small and medium enterprises is low and there is need to adapt it to these companies, especially in the context of the crisis generated by COVID-19. It presents a synthesis of specialized concepts, which are applicable to small and medium-sized companies, and which can be taken over and implemented by this types of companies. This paper analyzes the problems that have arisen at the company level, such as the suspension / reduction / ceasing of total or partial activity, problems related to supply, sales and delivery, problems questioning the existence of the company, as well as its short, medium and long-term sustainability. At the end of the paper, proposals are generated to support the sustainable development of small and medium-sized companies, in the epidemiological context generated by COVID-19.