This dissertation work presents an overview of ion channels for sodium and potassium for making a relationship with the biophysical, computational and mathematical. Studied in a qualitative way ion channels from the point of view of statistical mechanics, more precisely, considering the ion channel as a Markov process. The main objective of this work is to represent the dynamics of ion channels using the random walk and develop computer programs that simulate the operation thereof. We studied the departure of ions from the beginning of the channel (source) and its final arrival at a site (sink) a distance D. For the simulation of the channels for sodium and potassium were considered for the atomic masses of related chemicals, were not taken into account, the dynamic activation and inactivation of the channels, as well as the cellular structure. The importance of this work is to generalize the study of ion channels and thus seek parameters that could differentiate them. We also consider the importance of time, because we understand that real-time analysis is an important tool for understanding the behavior of biological systems. Finally, the essay ends with some simulation results of the channel for sodium and potassium to the reader and propose some future work.