Tokamak is known as a magnetic system for plasma confinement, where the plasma is heated and pressurized under the influence of powerful toroidal and poloidal magnetic fields. Currently, tokamak is one of the proper choices for generation of clean and low-cost energy, and it is anticipated that the construction of ITER as an international project in France fulfills the mankind dream for providing an economy energy resource. In this paper, we consider the equilibrium and transport problem in a tokamak plasma, and we study the numerical solution to the corresponding equations to achieve a desirable plasma configuration in Damavarid tokamak, of electromagnetic fields highly elongated cross section. Through the self-consistent combination of transport and equilibrium equations, we obtain a scenario for the temporal and spatial evolutions of plasma in Damavand. In particular, we noticed from the study of simulation data the existence of separatrix configuration in a small tokamak with elongated cross section and large aspect ratio. The separatrix configuration is a characteristic of advanced tokamaks including JET, and is regarded as an essential capability of these machines. This paves the way for designing a divertor for Damavand tokamak, to study the plasma-wall interaction, as well as mechanisms of energy extraction from plasma.