In this paper, two-dimensional (2D) defected ground structures (DGS) are proposed in microstrip line. The dumbbell structure is added as a unit-cell in a systematic manner in both horizontal and vertical directions to construct the 2D-DGS. This technique best utilizes the area to get very low stop band frequencies. The EM simulation has been carried out to study the transmission behavior of proposed structures. The variation of center frequency have been achieved from 9.42 GHz down to 4.1 GHz with more than 25 dB rejection in the stop band when the number of cells increases from 1 to 5 cells. We have also exhaustively studied the effect of DGS in horizontal and vertical directions in microstrip line. Further the proposed DGSs have been modeled as a parallel LC circuit connected in series to the main microstrip line. In order to validate model, the extracted circuit values with ADS circuit simulator has been used to compare the transmission behavior with EM simulation results obtained by IE3D. The comparison shows an excellent matching of EM simulation with equivalent circuit model.