Drug transport trough the skin might be considered an attractive route of administration due to its non invasive characteristics. The lack of mathematical models to properly represent, and thus understand the phenomena contributes to a timid use of this process in medical and cosmetic treatments. This work presents the development of an analytical representation for the transport of free drugs through the skin by a transient diffusion model for a homogeneous semi-permeable membrane. The equations were developed using non-conventional boundary conditions, considering resistance for mass transfer at the interface formulation-skin. The model considers the correct amount of drug being transported through the skin, therefore the decrease of drug content with time is taken into account. An analytical solution for the second Fick's law using these boundary conditions was obtained and equations for the concentration profile and flux of drugs through the skin are presented. The equations are a set of an infinite series of transcendental and exponential functions. The fitting of the parameters is not trivial and it uses the Maximum Likelihood principle. The Maximum likelihood principle leads to a system of non-linear equations. The use of more realistic analytical equations describing the drug transport through the skin should contribute to increase the understanding of the process of transdermal transport, allowing prediction of the required formulation amount in treatments as a function of drug properties and skin characteristics.