Following previous investigations on forced‐vibration methods of determining dynamic mechanical properties of viscoelastic materials, this article is proposing a similar technique for determining the complex Poisson's ratio and the complex dilatation constants. Through the study of forced vibration of a free viscoelastic sphere with internal harmonic oscillating source, it is found that the above mentioned properties of the test material are related to the ratio of the vibration amplitude of two measurable points. Thus, when using the criterion of this ratio approaching its maximum, the maximum amplitude ratio, these properties can be expressed in simple relationship with the laboratory‐measurable quantities: namely, the maximum amplitude ratios and their corresponding vibration frequencies. Investigations have been carried out for three sphere sets.