The elastic anisotropy of 5 cold-rolled steel sheets typical of automotive applications is probed experimentally and the results are represented using orthotropic elasticity. The steels have an increasing volume fraction of martensite, ranging from zero to over 90%. This leads to different strength and ductility for each of the 5 steels, with the strongest being 5.8 times so over the weakest, but only 0.11 times as ductile. The elastic properties measured are the Young's modulus and Poisson's ratio at 15° increments from the rolling direction of the sheets. These properties are measured by uniaxial tension and pure-bending experiments, respectively, instrumented with electrical-resistance strain-gages. The recorded responses are repeatable and, well within the limit of elastic deformations, linear. Both properties are found to have orientational dependence. The variation of the Young's modulus is the opposite of that of Poisson's ratio. In addition, the dual-phase (ferritic-martensitic) steels exhibit the opposite trends than the single-phase (purely ferritic) one. These experiments are then compared to the results of orthotropic elasticity. Under plane-stress, this material model depends on 4 material parameters. This simple model represents all of the experiments very well, indicating that the elastic anisotropy stems from the rolling-induced microstructure and, for the dual-phase steels, the presence of the second, reinforcing phase. Furthermore, the model allows the quantification of extension-shear coupling when these orthotropic materials are loaded off-axis to the material orientations. This coupling was found to be limited, so that the off-axis tension tests are indeed close to the uniaxial stress state. One of the material parameters needed is the in-plane shear modulus, which poses challenges in its determination for the present thin sheets. Despite the mild anisotropy found in these materials, assuming the isotropic value for the shear modulus deteriorates the predictions significantly. This work demonstrates that single- and dual-phase steels indeed behave elastically as orthotropic materials, as expected on theoretical grounds based on their pre-processing by rolling. The results of this work can be used to introduce elastic anisotropy in sheet metal forming simulations intending to predict springback, with only a limited number of experiments needed for calibrating the model for a given material.