Hydrogen production through electrolysis is an important research topic since the use of hydrogen as a fuel has the potential to significantly reduce gaseous emissions in near future. The electrolytic splitting of water into hydrogen and oxygen can be carried out using for instance electricity generated from renewable energy sources such as solar radiation. Electrolysis processes occurring in electrolyzer cells are complex phenomena and a clear and accurate mathematical representation of the referred processes is vital to accurate predict electrolyzer cells performance. So a comprehensive mathematical model capable of properly describing alkaline electrolyzer cells performance, in terms of efficiency and hydrogen production rate, is proposed in this work. The mathematical model is based on several physical concepts such as energy losses due to electron and ion transfer, entropy increase, electrolyte flow rate, and electrolyzer physical structure and construction material. Compared to existing models, the new proposed one is more complete as it includes more operational parameters (six) affecting cells performance. Once developed, the proposed model has been fine-tuned using experimental data available in literature. The results obtained using the new developed model are in good agreement with Ulleberg’s experimental data. Based on the work carried out here, it is concluded that developing a mathematical model based on physical principles is crucial in the comprehension of electrolysis related processes and how to utilize them in the simplest and most reliable way.