The shock wave structure is considered by embedding the Kelvin-Voigt type viscosity element in a rheological model of the elasto-plastic solid. The system of ordinary differential equations, which describes small intensity shock waves, worked out. Heteroclinic solutions of this system of equations are investigated. Types of bifurcations regarding the solution with respect to a change in the velocity of a shock wave are found. The series of nearly identity coordinate transformations is applied to evaluate the normal form. An integration of the normal form is reduced to the investigation of an ordinary differential equation of the first order. The conditions of solvability are established using the inequality of active plastic loading. Numerical simulations of a shock wave structure are performed. [References: 3]
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