This chapter explores the stress wave transmission and reflection from an incident stress wave, between isotropic solids of different Poisson’s ratio, with special emphasis on systems in which at least one of the solids is auxetic. The dimensionless transmitted stress, in terms of the ratio of transmitted to incident stresses, were investigated for longitudinal stresses in prismatic bars (1D stress), longitudinal stresses in width-constrained plates (2D stress or 2D strain), plane waves of dilatation (1D strain), torsional waves (shear waves), and Rayleigh (surface) waves. Each of these wave transmission study was performed under three special cases, i.e. when the (i) product of density and Young’s modulus for both solids are equal, (ii) product of density and shear modulus for both solids are equal, and (iii) product of density and bulk modulus for both solids are equal. Under these special conditions, results show that the stress transmission is effectively doubled or eliminated when the Poisson’s ratio for the isotropic solids are at their limits.