For the first time, an accurate analytical solution of mixed or contact problems for multicomponent multilayer materials has been constructed. It is assumed that the contact problem is formulated at the boundary of a multilayer multicomponent material in a semi-infinite region. These can be contact problems for a multilayer medium that simultaneously includes thermoelectroelastic, magnetoelastic, piezoelastic, water-saturated, nanomaterials and other layers described by linear partial differential equations. In the contact area, there can be any conditions of mechanical, physical or chemical properties that lead the boundary problem to a system of arbitrary finite number of Wiener-Hopf integral equations with a meromorphic matrix in the core. The article uses a new universal modeling method that allowed factorizing the operator of an infinite system of linear algebraic equations.