An urgent problem in the development of linear instruments of magnetic pulse attraction is to obtain practical recommendations for improving their efficiency, which is largely determined by the processes of current density distribution on the surface of sheet metals that are prone to deformation. The aim of the work is to calculate the characteristics and theoretical analysis of the spatial distribution of current on the metal surface of a flat sheet blank in the working area of a linear tool of magnetic pulse attraction when directly connected to the electrical terminals of a high voltage power source. To achieve this goal, a rigorous mathematical approach is used using the methods of electromagnetic field theory and methods of conformal transformations in the theory of functions of a complex variable. Formulas for numerical estimates are obtained, which quantitatively illustrate the distribution of currents on the surface of the sheet conductor at the contact connection of the power source. Based on numerical and graphical analysis of different geometric dimensions of this model, it is established that the level of current concentration flowing in the selected strip connecting the connection contacts significantly depends on the ratio of the width of this strip and the transverse dimensions of the contact connection. The part of the current that is directly involved in the excitation of force interaction between conductors with parallel currents in accordance with Ampere’s law is determined. The level of transverse current concentration, which flows mainly in the selected band, is ~ 65… 80 % of the total current, which has been confirmed experimentally. The obtained results allow us to conclude that it is necessary to conduct mandatory assessments of the level of concentration of the flowing current in the working area of the linear tool. Using the conclusions of this work will implement new, more efficient tools in pressure treatment technologies, namely, to create viable linear tools for magnetic-pulse attraction of specified areas of sheet metals when directly connected to sources of electric power.