The process of stress accumulation near earthquake faults during the aseismic period in between two major seismic events in seismically active regions has become a subject of research during the last few decades. In the present paper a long dip -slip fault is taken to be situated in a viscoelastic layer over a viscoelastic half space representing the lithosphere-asthenosphere system. A movement of the dip-slip nature across the fault occurs when the accumulated stress due to various tectonic reasons, e.g., mantle convection etc., exceeds the local friction and cohesive forces across the fault. The movement is assumed to be slipping in nature, expressions for displacements, stresses and strains are obtained by solving the associated boundary value problem with the help of integral transformation and Green's function method. A detailed study of these expressions may give some ideas about the nature of stress accumulation in the system, which in turn will be helpful in formulating an earthquake prediction programme
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