Strong discontinuities in solutions to nonlinear hyperbolic equation systems of continuum mechanics are considered. It is assumed that the mass flux through the discontinuity front is non-zero. If the number of boundary conditions that are to be observed on a discontinuity (which follow from conservation lows or other integral lows) is less than the number of unknown variables, then the discontinuity can be multiparametric. That implies that, if ahead of the discontinuity all the variables are known, then the state behind the discontinuity can depend on several parameters.In contrast, shock waves in gases the combustion fronts are one-parametric and zero-parametric discontinuities, respectively. It is argued that multiparametric discontinuities represent one of the common types in continuum mechanics. Two examples of problems of mechanics of deformable solids with multiparametric discontinuities arising in their analyses are considered. The structure of the discontinuities is considered and solutions of initial-boundary problems are constructed.
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