Recently, Graphene has attracted researchers' attention because of its exclusive thermal, mechanical and electromagnetical properties . Investigating the plasmons ' behavior in Graphene shows its potential to be a good substitute for noble metals i n plasmonics specially due to its controllable conductivity which provides more freedom in designing procedure for engineers. As a result, Graphene p eriodic arrays are very useful structures in frequency selective surfaces, Faraday rotators, polarizers, filters and so on. The absorbers which are very beneficial structures have been also affected by these new findings. Here we purpose to design and analyze Graphene terahertz absorbers using a lumped element equivalent circuit model . T he idea of presenting equivalent nano-circuits for plasmonic nano - particles was first proposed in 2005. A nano -particle behaves as an inductor or capacitor based on the sign of the real part of its permittivity to be negative or positive respectively. The imaginary part of the permittivity causes the losses and acts as a resistor. Thus , a nano-particle with a complex permittivity, could be modeled as an $ RC $ or $ RL $ lumped circuit . The permittivity of materials depends on frequency in some cases and we can approximate their behavior as an $ RLC $ circuit in which the incuctive or capacitive attitude dominates depending on the situation. Exactly the same idea can be used for a Graphene patch. This fascinating property provides us with the ability to modify the conductivity of different parts of a Graphene layer by adjusting the chemical potential in order to design arrays with desired characteristics. In this thesis , an analytical circuit model is introduced for an array of Graphene rings. To achieve the goal, the surface current density function is calculated on an isolated ring using quasi-static approximation. Then, the results are developed to a 2-D periodic array of Graphene rings by means of the first order perturbation theory. The surface boundary condition for electromagnetic waves together with the Rayleigh expansion is used to calculate the reflection coefficients and the closed form of the equations for the equivalent circuit elements , afterwards . The results are verified by comparing them with the ones derived from COMSOL software full wave analysis and the accuracy of the method is proved. Finally , we have benefited from the circuit model to design a wide-band absorber. Introducing a closed form for the equivalent lumped circuit of a Graphene periodic array as a function of its structural and geometric parameters, helps us to design or improve them for more desirable results, more facilely. This will be helpful in designing absorbers as well. Absorbers are very useful structures in sensing , imaging, photodetection and cloaking applications . Graphene , Periodic Arrays , Absorbers , Lumped Element Equivalent Circuit