Rapid population growth, urbanization and industrialization simultaneously increased the need for drinking water, as well as the intensity of their pollution. The biggest problem is considered to be the wastewater from industries that pose an extra burden on recipients of such water due to the high content of organic and inorganic substances. The ever-increasing industrial production of olives and olive oil production has resulted in increased wastewater content generated from this industry (eng. Oil Mill Wastewater, OMW). Such wastewater contains extremely high concentrations of phenols and polyphenols, such as tyrosol, which pose a particular environmental hazard because of the decomposition of oxygen consuming water, disturbing the natural equilibrium ecosystem. For these reasons, over the last few years, research in the field is focused on finding an economical and efficient process for processing such wastes. From an ecological point of view, the catalytic oxidation of hydrogen peroxide (eng. Catalytic Wet Peroxide Oxidation, CWPO) was demonstrated as alternative method to classic wastewater treatment. In this process, the hydroxyl radicals formed by the degradation of hydrogen peroxide oxidize the organic molecules with which are these waters rich in content. The excess of hydrogen peroxide is not a problem because it spontaneously decomposes on water and oxygen and does not harm the environment. By adding the catalyst, the reaction can be accelerated and made economically more acceptable because the process can then effectively be carried out at atmospheric pressure and temperatures below 353 K. In this work CWPO method is used on a model pollutant (aqueous solution of tyrosol), in batch and plug flow reactor. The catalyst that was used, Cu/13X-K1273, showed good catalytic properties in the process such as activity and thermal and chemical stability. The particular interest of this paper is to investigate the possibilities of implementing the CWPO process in continuous reaction systems such as a plug flow reactor with a catalyst support layer. Kinetic analysis was performed using an integral parameter estimation method assuming that tyrosol breakdown kinetics can be described by either the first order of tyrosol or second order reaction taking into account another reactant hydrogen peroxide.