The work is dedicated to the development of a new downhole resistivity microimaging tool for logging while drilling (LWD) in oil and gas wells. The purpose of this research is to create algorithms and software for mathematical modelling of tool signals and to define the area of its application using realistic geoelectric models. In order to study the possibilities of the tool in the proposed configuration, the algorithm and the software for 3D simulation of electrical signals have been developed. By utilizing this software the mathematical modelling of the LWD resistivity microimager signals have been performed for realistic geoelectric models: an inclined boundary of the layers with different resistivity and a horizontal fracture filled with a conducting drilling fluid. An analysis of the simulated signals shows that the tool can detect thin fractures or layers with a thickness similar to the diameter of the current electrodes. The application of standard interpretation techniques to the obtained images showed that the inclination angle of the intersected boundaries can be determined with the accuracy of ±2°.