Magnetic Resonance Electrical Impedance Tomography (MREIT) is a technique to image the electrical conductivity distribution inside the object (such as a human body). This technique consists of three steps: current injection into the object, the measurement of the magnetic flux density by a Magnetic Resonance Imaging (MRI) system, and the reconstruction of the conductivity distribution from the measured magnetic flux density. Although there are other algorithms to reconstruct the conductivity distribution inside the object, in this thesis, the Sensitivity Matrix Method is investigated for 3D problems. In MREIT, the use of the Sensitivity Matrix Method is not common for 3D problems. This is because of the fact that for 3D problems the Sensitivity Matrix Method requires large memory space and long calculation time. Calculation of the sensitivity matrix is the most time consuming part of this method. Therefore in this thesis, a modification is proposed in order to reduce the calculation time of the sensitivity matrix. Since the sensitivity matrix will be calculated at each iteration, this modification speeds up the algorithm significantly. Also by making several assumptions regarding the conductivity distribution of the object, the problem may be further reduced. In this thesis, conductivity distribution inside the object is assumed to be z-invariant (z is the direction of the main magnetic field of the MRI system).Thus the dimension of the sensitivity matrix and the time required to calculate the conductivity distribution inside the object significantly decrease. Another problem with the application of the Sensitivity Matrix Method is that the magnetic flux density calculated by subtracting the calculated magnetic flux density (for the assumed initial conductivity distribution) from the measured one has errors. These erros are results of the boundary mismatches between the simulation object and the real object, inaccuracies in calculations and measurement artifacts. In this thesis, use of a multichannel current source is proposed in order to reduce these errors. Using the multichannel current source not only reduces the errors due to the boundary mismatches and other reasons but also sustains a nearly uniform current distribution inside the object.