<p>This study focuses on permanent surface dislocations caused by a strike-slip fault in an alluvial valley. A two-dimensional mathematical model is utilized, considering the valley to have a half-cylindrical shape. The valley medium is assumed to be isotropic, linear elastic and nonhomogeneous, such that the shear modulus of the valley has spatial dependency. The valley is surrounded by an isotropic, linear elastic and homogeneous half-space. A strike-slip fault is located at the intersection between the valley and the half-space. The problem is solved analytically by using finite Fourier transform. Displacement functions are obtained in closed-form, in terms of power series and hypergeometric function series. Unknown coefficients of these series are determined from the boundary conditions, leading to an analytical exact solution. Numerical results indicate that the nonhomogeneity of the alluvial valley material has a limited impact on permanent surface dislocations unless there is a significant variation in the material properties within the functionally graded zone. In many cases, approximating the nonhomogeneous alluvial valley as a homogeneous medium is suitable.</p>