Electrical Impedance Tomography (EIT) is an easy, low cost and safe method for capturing medical images. Its main goal is to finding the electrical properties of a body tissue. Knowing electrical properties of any organ of human is very important and useful for medical science Using medical images obtained from EIT. A tomographic medical image has been constructed through processing of measurement data that could help to obtain electrical properties of tissues. Forward and inverse problem are two famous problems in EIT. In Forward problem, the voltages and currents are computed to solve EIT problem, but in inverse problem, conductivities are obtained. In fact solving of inverse problem leads to image reconstruction. Block method (BM) is a known technique to solve EIT problems. In this technique, tissue is modeled first by some blocks. It is assumed that each block has a constant conductivity (or resistance). A tomographic imaging is constructed by calculation of its conductivity. Recently a non-iterative linear inverse solution is presented for block method, which we name 2D BM; however the method has not been upgraded yet. In this article, several efficient algorithms with new formulations is proposed to improve the 2D BM. To examine the proposed method, several examples have been investigated. Results show that suggested algorithms could achieve superior outcomes in all situations while its run time is increased . Three algorithms such as improved block method, expanded block method and combined block method has been proposed in this thesis. These three algorithms cause significant error reduction respectively. In the case of 5x5 block, error in 2D BM is between 30.31 and 559.74 but in improved block method, expanded block method and combined block method algorithms this error bands are 8.9-23.49, 0.0028-0.87 and 0.00024-0.02 respectively. As results shown, error value in expanded block method algorithm is reduced less than 1 and error in combined block method is decreased well below 5 percent. Keywords: Electrical Impedance Tomography (EIT), 2D block method, forward Problem, Inverse