A relationship between the time-dependent shear and bulk modulus and stress and strain uniaxial creep compliance is derived on the basis of the constitutive convolution itegral equations. Next, a new method for identification of the time-dependent shear and bulk modulus of linear viscoelastic materials, using discrete time-measurements of the uniaxial creep compliance of unconfined and a laterally constrained cylindrical specimens of the material obtained in double creep experiment is developed. The least-squares method is applied to approximate the uniaxial creep compliance. An analysis of the creep compliance model accuracy is conducted for noise measurements and the linear rate of convergence of the approximation scheme is proved. In general, the method requires numerical inversion of the Laplace transform of the shear modulus, however in the case of five-element Kelvin models an exact analytical solution is obtained. The shear and bulk modulus can be described as a linear combination of constant and exponential functions and multiple convolution integrals of original and modified Bessel functions. A resulting simple identification scheme is outlined. The effectiveness of the method is demonstrated through the computation of the time-varying shear and bulk modulus of the sugar beet root samples.