The variety of accidents which happen during the construction of oil and gas wells causes the expansion in the use of magnetic fishing tools. However, the known tools based on permanent magnets have a significant drawback involving the flat working surface of the magnetic system that does not permit to achieve a considerable attraction force to a fished object of complex geometric shape. Therefore, the aim of the research is to increase the efficiency of removal the objects of irregular geometric shape from the wells by enlarging the area of contacting them. For that purpose, it has been developed a fundamentally new design of the large-diameter fishing tool with the moving magnetic systems capable of copying the shape of the objects to be fished. Each magnetic system, which is compound of permanent rare-earth neodymium magnets and concentrically placed magnetic cores, shall be held by the magnetic field of adjacent systems with opposite polarity. There were conducted theoretical studies using the finite element method to determine the working capacity of the designed tool. As a result, it has been found the value of hoisting capacity during the interaction of magnetic systems with the roller cone of the drill bit; this fact confirms the capability of fishing the objects of irregular geometric shape. In addition, it has been explored the influence of the material of the fished object on the power characteristics of magnetic systems. The application of the designed magnetic tool allows removing the ferromagnetic objects from the well regardless of their shape, weight and position on the bottom hole. Apart from that, the given tool may be used in the areas where the technology of work is related to drilling wells.