The generalized Maxwell model, which describes stress relaxation modulus, is usually used for analyzing the rheological characteristics of viscoelastic materials.

In terms of Laplace transform,the relation of creep compliance and relaxation modulus can be inferred.

In this paper Laplace transforms is utilized in viscoelastic theory of polymers making the relations between various viscoelastic functions like relaxation modulus, creep compliance and functiqns representing dynamic behavior simple and clear, relaxation spectrum and retardation spectrum are defined in terms of Laplace transform to correlate all viscoelastic functions.

Secondly, by doing many modeling tests about rapid relaxation inversion(RRI),OCCAM inversion and nonlinear conjugate gradient inversion(NLCGI),we did research on the following characteristics: the relation between initial model and imaging effect, the stabilization of the convergence process and the dependability of the inversion result.

On the basis of viscoelastic theory,inversion of Laplace transform and numerical calculation is applied in the calculation of bulk relaxation modulus K(t) for solid propellants through the tension relaxation modulus E(t) and viscoelastic poisson ratio v(t).