In the begining of this paper a classification of costs is made, and costs are defined as is the terminology that is connected to them. The paper then moves towards cost management and then comes to costing methods. In the next part is a deliberation between traditional and modern costing methods, of which the ABC costing method is a part, and each of them is briefly described. In the theoretical part ABC method is more closely defined, as are the steps for its implementation, its advantages and disadvantages and historical phases of development and the role it plays in a company today. The empirical part consists of a cost calculation based on the company CEMEX Hrvatska d.d. which uses a process based costing method to determine if the implementation of ABC will result in lower unit production costs. In the conclusion part of this paper the findings of this paper are laid out, and based on the research it's concluded that implementing the ABC costing method is not economical for the company CEMEX Hrvatska d.d. to implement it. Rather, it is more cost effective to use the process based method it is using right now, because of the ratio of overhead costs in the total costs of the company, homogeneity of its products, and therefore, its production activities, and the costs of reorganisation that implementation of ABC would incur on the company.