Designs of linear generators with permanent magnets for electric shock absorbers are considered. The inductor or armature is moved by generators with a fixed armature and the generators with a fixed inductor. Generator armature windings are used to stack windings in slots and slotless windings. The method of placing permanent magnets on the inductor and the method of their magnetization are used to create inductors with magnets located on the surface and magnetized radially and the inductors with magnets located inside the inductor and magnetized in the axial direction. The design of generator with the winding located in the slots of the inductor and with the magnets on the surface was chosen as being most optimal from the point of view of manufacturing technology. To study the dynamic modes of an electric shock absorber, a mathematical model was developed in the MATLAB/Simulink software package. It is a characteristic of the model that standard blocks of expanded Simulink software are used for mathematical description of the reciprocating linear generator, battery, behavior of load changing, and device for switching the generator from the battery to the ballast resistance: a generator model based on a rotary electric machine with permanent magnets, the model of the battery, the model of the disturbing force, and the model of the transistor. For adequate description of the processes in the rotary and reciprocating generators, a system was developed to recalculate their parameters based on the equality of mechanical powers of generators and kinetic energies of their moving parts. Since mathematical equations of the generator, batteries, and load are contained within the program blocks, their use makes it possible to study in detail the transient processes when different laws of variation of disturbing force, generator parameters and battery types, since it is necessary merely to set the input parameters of the program blocks. The results of mathematical simulation of an electric shock absorber under the action of a shock disturbing force are presented.