Abstract
In this paper, the problem of static deformation of an initially stressed medium with irregular thickness, using eigenvalue approach has been considered. The irregularity is expressed by a rectangle shape. As an application, the normal line-load acting inside an irregular orthotropic half-space has been considered. Further, the results for the displacements and stresses have been derived in the closed form. To show the effect of initial stress and irregularity, variations of the displacements with horizontal distance are shown graphically for different values of irregularity size and stress parameter. It was found that the initial stresses as well as irregularity affect the deformation significantly.