We study the anomalies of elasticity (negative values of Poisson’s ratio), which take place in auxentic foam materials. To analyze the deformation of auxentic material, we use elastic rods to simulate a structural unit. In order to estimate the values of Poisson’s ratio, we use two methods for calculation of parameters of uniaxial tension. In the first case, the model is defined directly by the relationships between stress tensor and strain tensor by means of solution of system of equations. In the second case, we use a finite element method for estimation of transverse and longitudinal displacements of a rectangular fragment (sample) of foam material. The results of comparison prove us that the difference of Poison’s ratios obtained by these two methods, does not exceed 10%. We study the dependence of Poison’s ratio on the direction of loading and the parameters of the reinforcing rods. It is discovered that the values of Poison’s ratio estimated by the model proposed can become negative in some directions, i.e. the model is anisotropic.