Mathematical modeling and analysis of biological systems leads to attain further knowledge in biological fields and thus pave the way for prevention and treatment of diseases. Particularly, in the last two decades, engineering and applied mathematics has been widely used in modeling and analysis of biological networks. Among various techniques for modeling and analyzing biological systems, Petri nets, due to their computational and graphical capabilities, have attracted much attention. Flexibility and simplicity of these nets along with their ability to model simultaneous reactions, has made these nets the suitable tool for modeling biological systems. Signal transduction pathways are sets of processes that enable the cell to communicate with its various departments and also adjacent cells. One of the signal transduction pathways of a cell is the TGF-? pathway. . Any interruption in this signal transduction path may be followed by cell destruction. In this thesis, a stochastic Petri net model of the signal transduction pathway based on scientific knowledge and experimental data is proposed. The main purpose of modeling the transduction system, is to search the response range of the system to investigate the ability of the system to produce experimental data obtained from in vivo experiments. In spite of the ability of the Petri model to justify and reproduce the experimental data, it seems another modeling tool with more computational capabilities might be needed. For example to perform sensitivity or centrality analysis, Petri nets do not offer proper computational tools. Differential equations on the other hand are an appropriate choice in this matter as they provide more computational and analysis options. For example to perform sensitivity analysis differential equations provide straight forward computational options compared to Petri nets. So, a system of differential equations is presented to describe the signal transduction pathway. By comparing Petri model and the system of differential equations representing the TGF-? pathway and also their output responses with experimental data, advantages and disadvantages of each modeling method is investigated and compared. Although Petri nets do not enjoy the vast computational capabilities of differential equations, their ability to model qualitative and quantitative features of the system in one model, makes them more appropriate for modeling biological systems in which many aspects are qualitatively known. In the discussed signal transduction pathway, increment of certain proteins in the cell, leads to cell destruction. Experimental results also confirm the incident. Next, a standard Petri net-based controller is proposed to control the increment of these proteins thus cell growth. The results are translated to the form of stoichiometric equations for the usage of biologists. Keywords: TGF-? signaling pathway, Stochastic Petri nets, Modeling biological pathway, Control, P-invariants, System biology, Cell