According to published statistics regarding pharmaceutical industries, there has been a significant increase in the demand for cosmetics and skincare products. As a result, there has also been an increase in interest by researchers to conduct experimental and theoretical studies on these industries. The outermost layer of the skin, which is the stratum corneum, plays a key role in determining the skin permeability. This layer represents the first and main barrier against dehydration and screening from external elements and pathogens. Research efforts have been made to better understand skin permeability. Experimental methodologies play a key role in pharmaceutical and dermatology studies. However, ethical standards of using animal and human models in in-vitro permeability studies are very strict in their admission process and approval time. Furthermore, the lack of available material and financial resources for setting up, operating and repeating experiments has also limited the required progress. These problems can be addressed by developing better mathematical models on skin permeability. Progress, regarding the mathematical modelling of solute transport in skin, has been achieved in the last decades. The mathematical modelling strategy is used as a skin permeability predictor tool based on common physicochemical properties of the skin and penetrated solute molecules. Many factors play an important role in the formulation of a mathematical model and in determining how reliable the predicted results are. Therefore, the more skin physiological details are included in the model, the more computational efforts are required to interpret the solute permeation mechanisms in the dermal region and simulate a drug transport in the transdermal administration. The mathematical complexities associated with formulating a mathematical model of drug transport in skin significantly limit the utilities of such models in practice. Thus, a balance between the model’s complexity and how realistic it is in describing the solute transport processes in skin has to be achieved. Therefore, a mathematical model formulated on principles familiar to the pharmaceutical scientific community could be of value. In this thesis, we have developed a novel mathematical model using a compartmental approach. The proposed model enables for simulating solute transport across the stratum corneum (SC) in a variety of exposure scenarios in percutaneous drug delivery systems. The obtained results were compared with the diffusion model outcomes – which can be considered the current ‘golden standard’ for modelling skin transport – and showed a good agreement. The mathematical foundations of the model are relatively simple and better aligned with the physiology of the stratum corneum. In addition, this work shows that performing a numerical simulation using the compartmental model is less demanding than using the diffusing model, especially for complex exposure scenarios, and can be performed using free software, such as Python. The research findings of this thesis contribute towards a better understanding of transport phenomena across the skin. Also, the compartmental model proposed in this work can be used to describe transport phenomena in the membrane. Due to the similarity between the governing equations of diffusion and heat transfer, the proposed approach also offers a mathematical framework for studying heat transfer problems in biomaterials with minimum model development or computational efforts.