Combined numerical and analytical determination of overall dynamic response and creep behavior of random multi-component reinforced elastomers are proposed. Magnetorheological elastomers are considered here as an example of smart materials, composed of micro-sized magnetic carbonyl iron particles dispersed in a non-magnetic silicone rubber. The viscoelastic behavior of rubber matrix is described by Rabotnov’s type quasi-linear law. The random structure of composite analyzed, so constitutive equations for statistical fluctuations of first and second order displacement, nonlinear Green deformation, nominal or Cauchy stress in the representative volume are used. Upon application of the integral Laplace-Carson and Fourier transforms, the boundary value problem for the local stress and strain fields becomes similar to a nonlinear elastic one. The volume concentration of carbonyl iron remains unchanged after transforming from the time domain to the Laplace-Carson domain, as in the case of non-aged materials. The explicit determination of the inverse transform is not straightforward, and numerical methods are required. Efficient algorithms for numerically evaluating the inverse Laplace transform we use here from NAG-Fortran library. Numerical experiments by finite elements modelling were carried out with the aim of choosing the optimal structure and composition of multi-component magnetorheological elastomer materials.