Abstract We have performed a molecular dynamics study in order to verify the assumption that saturated hydrocarbons can be characterized by generalized Hook׳s law using the fourth rank tensor of elastic constants. In this study normal paraffins were treated as crystals of hexagonal symmetry. Thus, we obtained original numerical values of Young׳s modulus and Poisson׳s ratio in both anisotropic and isotropic planes and the values of the shear modulus at three different temperatures. Negative Poisson׳s ratio of n-paraffins is of a particular interest. The author believes that auxetic behavior of saturated hydrocarbons is the result of their liquid-crystalline nature. Another remarkable point is the non-linear elasticity of n-paraffins detected in a wide temperature range. This provides an additional experimental confirmation of the phase transition process of hydrocarbons earlier reported in scientific works. We have shown that the matrix of elasticity of a particular heavy petroleum product can be estimated using the elastic parameters of the n-paraffins obtained. The numerical values of five independent elastic constants are directly proportional to the composition of a heavy petroleum product. The simplified representation of the composition can be defined by a few saturated hydrocarbons with different carbon numbers. The numerical results obtained in this research may be useful for those interested in heavy petroleum fractions rheology as well as those who perform numerical studies in petroleum hydrodynamics and acoustics.