Within the framework of integral constitutive relations for linear isotropic viscoelastic media with difference-type kernels in the case of a non-relaxing volume, possible, complementary to the known, setup experiments for determining the kernels of the Ilyushin operators ˇ gβ are proposed. One of them is based on the use of a sample from an auxiliary viscoelastic material, the material functions of which are related to the creep function and the volume compression modulus of the source material. Similar schemes of setup experiments for finding the kernels of ˇℎ γ operators, in a certain sense conjugated with ˇ gβ, are also proposed. A scheme of a quasi-static experiment in a linear viscoelastic isotropic cylindrical layer is presented, where there is a state in which shear creep and shear relaxation are realized simultaneously in two orthogonal directions to each other. The outer surface of the layer is stationary, and by setting tangential displacements and shear stresses on its inner surface in a certain way and measuring the remaining components on the same surface, it is possible to experimentally confirm the integral relations of the reciprocity of the shear creep and shear relaxation functions.