The mathematical aspects of the problem of the interpretation of the experimental data on the viscoelastic behaviour of materials by making use of the linear and quasi-linear relaxation model proposed by Fung, are considered. Three idealized cases of the growth of the strain from the zero value of its value a = const., that it will keep at t ≥ t₀, are analysed: Case 1—a jump at t = t₀, Case 2—a linear law of growth in the interval 0 ≤ t ≤ t₀, Case 3—a parabolic law of growth in the same interval. The exact formulae for calculation of the stress are presented. From them the simple ‘small time’ and ‘great time’ asymptotic expressions are derived. These expressions are used for comparison of the Cases 1, 2, 3. An algorithm is suggested for the iterative numerical evaluation of the parameters of the linear model on the basis of the experimental data, corresponding to Case 1, 2 or 3.