The article discusses the stresses around a fault or crack in dissimilar media, focusing on the behavior of stress near a crack between two different isotropic homogeneous materials. The study extends previous work on symmetrical or antisymmetrical loading of a homogeneous plate with a crack to the case where the crack separates two different materials. It is found that the modulus of the singular stress behavior remains proportional to the inverse square root of the distance from the crack tip, but the stresses exhibit a sharp oscillatory character of the form $r^{-3} \sin(b \log r)$, confined close to the crack tip. Additionally, a shear stress along the material interface exists when the materials are different. The problem is considered in the context of geological investigations involving fault lines at the interface of two rock layers, and also applies to weld joints with cracks along the original weld line. The geometry involves two materials, $M_1$ in the upper half-plane and $M_2$ in the lower half-plane, joined along the positive $x$-axis. The elastic plane stress solution is sought for unloaded edges along the negative $x$-axis. In the homogeneous case where $M_1 = M_2$, the stresses near the crack base become mathematically infinite according to an inverse square-root law, $\sigma \sim r^{-1}$. However, when the materials are different, the stress behavior changes, leading to oscillatory stress patterns. The solution involves a biharmonic stress function $\chi(r, \psi)$ that satisfies certain boundary conditions. The resulting equations lead to a determinant condition for the existence of non-trivial solutions, which is analyzed to determine the eigenvalues. In the homogeneous case, the eigenvalues are $\lambda = (2n+1)/2$, with the lowest eigenvalue being $\lambda_{\min} = 1/2$, leading to stress behavior $\sigma \sim r^{-1}$. For different materials, complex eigenvalues are considered, leading to oscillatory stress patterns. The results show that the stress behavior near the crack tip is similar to the homogeneous case, with the maximum modulus of the stress determined by $r^{-1}$. The study also discusses the implications of these results for geological and engineering applications, including the distribution of strain energy around a fault and the qualitative agreement with observations of energy release. The findings suggest that high strain concentrations occur at the ends of a fault, with the energy distribution not being uniform around the crack tip.The article discusses the stresses around a fault or crack in dissimilar media, focusing on the behavior of stress near a crack between two different isotropic homogeneous materials. The study extends previous work on symmetrical or antisymmetrical loading of a homogeneous plate with a crack to the case where the crack separates two different materials. It is found that the modulus of the singular stress behavior remains proportional to the inverse square root of the distance from the crack tip, but the stresses exhibit a sharp oscillatory character of the form $r^{-3} \sin(b \log r)$, confined close to the crack tip. Additionally, a shear stress along the material interface exists when the materials are different. The problem is considered in the context of geological investigations involving fault lines at the interface of two rock layers, and also applies to weld joints with cracks along the original weld line. The geometry involves two materials, $M_1$ in the upper half-plane and $M_2$ in the lower half-plane, joined along the positive $x$-axis. The elastic plane stress solution is sought for unloaded edges along the negative $x$-axis. In the homogeneous case where $M_1 = M_2$, the stresses near the crack base become mathematically infinite according to an inverse square-root law, $\sigma \sim r^{-1}$. However, when the materials are different, the stress behavior changes, leading to oscillatory stress patterns. The solution involves a biharmonic stress function $\chi(r, \psi)$ that satisfies certain boundary conditions. The resulting equations lead to a determinant condition for the existence of non-trivial solutions, which is analyzed to determine the eigenvalues. In the homogeneous case, the eigenvalues are $\lambda = (2n+1)/2$, with the lowest eigenvalue being $\lambda_{\min} = 1/2$, leading to stress behavior $\sigma \sim r^{-1}$. For different materials, complex eigenvalues are considered, leading to oscillatory stress patterns. The results show that the stress behavior near the crack tip is similar to the homogeneous case, with the maximum modulus of the stress determined by $r^{-1}$. The study also discusses the implications of these results for geological and engineering applications, including the distribution of strain energy around a fault and the qualitative agreement with observations of energy release. The findings suggest that high strain concentrations occur at the ends of a fault, with the energy distribution not being uniform around the crack tip.