Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality providing cross-sectional images of a conductivity distribution inside an electrically conducting object. MREIT has rapidly progressed in its theory, algorithm and experimental technique and now reached the stage of in vivo animal and human experiments. Conductivity image reconstructions in MREIT require various steps of carefully implemented numerical computations. To facilitate MREIT research, there is a pressing need for an MREIT software package with an efficient user interface. In this paper, we present an example of such a software, called CoReHA which stands for conductivity reconstructor using harmonic algorithms. It offers various computational tools including preprocessing of MREIT data, identification of boundary geometry, electrode modeling, meshing and implementation of the finite element method. Conductivity image reconstruction methods based on the harmonic $B_z$ algorithm are used to produce cross-sectional conductivity images. After summarizing basics of MREIT theory and experimental method, we describe technical details of each data processing task for conductivity image reconstructions. We pay attention to pitfalls and cautions in their numerical implementations. The presented software will be useful to researchers in the field of MREIT for simulation as well as experimental studies.