This paper demonstrates that qualitative reasoning plays a crucial role for both an efficient and physically correct approach to the automated formulation of an accurate quantitative model which explains a set of observations. The model which "best" reproduces the measured data is selected within a model space whose elements are constructed by exploiting specific knowledge and techniques of the application domain. An automated search, performed at a pure numeric level through system parameter identification methods, may be inefficient because of the computational costs which significantly grow with the dimension of the model space. Even more importantly, a "blind"search over the whole space may yield a model which best fits the observations but does not capture all of the qualitative features of the physical system at study, such as for example discontinuities of the behavior. We approach the selection problem by exploiting a mixture of qualitative and quantitative techniques which require both symbolic and numeric computations. This paper illustrates the suitability of such an approach in the context of a computational environment for the automated formulation of the constitutive law of an actual visco-elastic material.