The paper considers some problems of calculating spectral characteristics of magnetic field of the linear induction motor (LIM), operating at the electrical braking modes. In automatic drives with LIM the electric braking modes are usually applied: dynamic, recuperation, single – phase, capacitor type, braking by means of opposite connection, by pulsating current and inverter type (frequency) braking. During the process of braking in the moving part of the LIM and in some cases in an inductor there are initiated complicated interrelated electromagnetic and electromechanical non – stationary processes. The braking processes have been analysed in the motionless right – sided Descartes system of coordinates x, y, z. There have been presented the expressions of volumetric density of braking current which have been regarded the non – periodic functions of coordinate x. Besides that in cases of single – phase and capacitor braking these expressions are also regarded as the non – periodic functions of time. Therefore when compiling the mathematical model there have been applied Laplace and Fourier integral transformations. After having applied Fourier transformation there have been received the expressions of the spectra amplitudes of primary magnetic field at the dynamic braking under the condition that the number of excited zones in the inductor is even, uneven and fractional. The continuous spectra of amplitudes have been calculated by the software Mathcad 2001 Profesional.