Cost management represents a special aspect of economics and management that aims to optimize and control costs in order to maintain competitiveness and stay within budget. In the theoretical part of the thesis, concepts such as costs, cost allocation, cost management methods, and the concept of the public sector and its components are explained. Various research methods were used in preparation of the work, including analysis and synthesis method, the historical method and others.In order to better explain the concepts related to costs and costs management methods, they are presented using the Croatian Post Corporation as example. In research part of the paper the cost structure of Croatian Post for the period from 2019 to 2021 is presented. Due to pandemic of the COVID-19 virus, there are visible changes in the expenses of the Croatian Post, which are detailed in the research part of the thesis. The purpose and goal of this work is to show how the use of traditional and modern cost management methods affects the organization's operations. The results show how in the Republic of Croatia, the traditional cost management method is still mainly used, which was proven by the example of Croatian Post. Due to accelerated changes in the market and new business methods based on advanced technologies, companies must be prepared to follow these changes. It is necessary to constantly work on improving the cost control process in order to ensure the efficiency and profitability of the company's operations. For this reason, it is essential to continue research.