<p>A nonconservative model of a shared-pressure multivelocity multicomponent heterogeneous medium with compressible and incompressible fractions has been proposed whose differential equations are based on the laws of conservation of mass, momentum, and energy for the entire mixture and its individual components. To exclude the "parasitic" smearing of contact boundaries, the parameter ξ has been introduced into the equations of the mixture′s model; it is proposed that this parameter be selected small and nearly zero. The characteristic analysis has been made of the equations of the model and its hyperbolicity has been shown at the parametric values ξ ∈ (0, 1]. In integrating the model′s equations, use has been made of the multidimensional nodal method of characteristics which is based on the splitting of the initial system of equations by coordinate directions into a number of one-dimensional subsystems, each being solved with the inverse method of characteristics. Using this method, a number of one-dimensional and two-dimensional model problems have been calculated.</p>