We propose a novel relaxation scheme for the simulation of compressible material flows at all speeds. An Eulerian model describing gases, fluids and elastic solids with the same system of conservation laws is adopted. The numerical scheme is based on the relaxation technique introduced by Jin-Xin. The linearity of the transport operator in the relaxation system allows for an easy implementation of a fully implicit time integration. The spatial discretization is obtained by a combination of upwind and centered schemes, in order to recover the correct numerical viscosity at all Mach numbers. Thanks to this, the scheme is very accurate in approximating material waves at all speeds. Moreover, the acoustic CFL constraint may be avoided without facing stability issues. The proposed scheme is the same for all materials and can handle different Mach regimes. Gas and liquid flows and hyperelastic solids deformations have been simulated at different speeds. Multimaterial applications are currently under investigation.