Abstract. The carbon tax legislation has been widely advocated as a cost-efficient law to push companies to reduce their carbon emission through their supply chain’s (SC) activities. Based on a carbon emission reduction’s target, different carbon taxation strategies have been implemented around the world. Generally, governments launch the carbon tax with a relatively low carbon price and plan to increase it incrementally over years adopting various strategies in a way to attend their emission reduction objective. The majority of developed mathematical models within green supply chain design (GSCD) under carbon tax legislation have ignored the dynamic aspect of this legislation. We believe that companies when designing their SCs have to consider not only the actual applied carbon price but also the eventual evolution of this carbon price over years. We aim to contribute to literature by studying the impact of the dynamic carbon tax legislations on the strategic decisions of a SC mainly the technology investment decision. Our objective is to illustrate that the dynamic modeling approach is more appropriate to study such strategic problems than static modeling. We develop a dynamic model of technology selection under progressive carbon tax legislation. Through a numerical example, we solve the dynamic model and we compare it with the static model. To do so, this static model has been tested under three different values of the carbon taxes mainly the launch carbon tax value, the average carbon tax value and the final target carbon tax value. We compare the efficiency of the used modeling techniques to guarantee a more visibility for the company and provide it with performant decisions that allow greening their SCs and saving its profit.