Two vertical, interacting, creeping,, strike-slip faults – one, buried and the other surface breaking situated in the upper layer of a layered model of the lithosphere-asthenosphere system, consisting of an upper elastic layer in. welded contact with a visco-elastic half space below it, is considered. Solutions are obtained for the displacements, stresses and strains in the model during aseismic periods in the case when no fault is creeping, the case when one fault is creeping and the other is locked and the case when both the faults are creeping. The effect of seismic fault creep across one fault on the shear stress near the faul itself is investigated together with the effect of creep across the other fault. Some situations are identified where aseismic creep across one fault results in the release of shear stress near the other fault, reducing the possibility of seismic movements across it. Other situations are also identified where aseismic creep across one fault results in the accumulation of the shear stress near the other fault increasing the possibility of seismic faults movement s. The possible uses of the theoretical model in obtaining greater insight into earthquake processes in seismically active regions with interacting faults are examined.