A combined study of microstructure and mechanical properties for a series of single‐site metallocene ethylene/1‐hexene copolymers is presented. The analysis of the results focuses on the effect of branching, which in turn modulates crystallinity and density, on the values of the elastic modulus obtained in tensile‐deformation experiments. An extensive literature review is done in order to compare our own results with previous studies. The typical variation found in the elastic modulus is discussed in terms of the existence of a rigid amorphous phase. This rigid phase controls the macroscopic mechanical behavior of the materials, giving rise to an increase of the elastic modulus as the crystallinity does. Mechanical coupling models for heterogeneous systems are applied in order to describe the experimental results of the elastic modulus as a function of the variation of three different phase fractions, i.e., crystalline, rigid amorphous (or interfacial), and mobile amorphous. The phase fraction values obtained from the analysis of the mechanical properties are in qualitative agreement to those found experimentally in our group by Raman infrared spectroscopy and from the literature by positron annihilation lifetime spectroscopy. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013