The coffee industry is worth over 100 billion dollars a year, making it one of the most valuable market in the world. Over the years, various scientific studies have been carried out to improve the quality of the cup of coffee. In fact, several mathematical models have been developed to describe the different physical processes in the coffee extraction. Another fundamental step in improving the final quality of coffee, which takes place before the extraction phase, is the roasting process. The roasting of green coffee beans is a complex process involving several chemical reactions that are crucial to determining the colour, taste and aroma of coffee. It consists of three main steps: drying, roasting and cooling. During these stages, the coffee bean is subject to heat and mass transfer. The transfer of the heat during the roasting of coffee beans significantly influences the flavour profile of espresso coffee. The main chemical reaction that occurs during roasting is known as “Maillard reaction”. This plays a fundamental role in the sensory profile and safety of the roasted coffee. In this study, a mathematical model for coffee roasting and its numerical approximation is proposed. The model is applied to determine the Maillard reaction products and the substances concentration in the roasted coffee beans at different temperatures and over various time periods. The research is validated through the use of real data, based on chemical analyses on coffee samples extracted during various phases of the roasting process.