<p>Most of the earthquakes occur when there is a movement along faults within the earth. It is more often observed that more than one fault is situated in seismically active regions, and a movement across any one of them affects the nature of the stress accumulation near the neighboring fault. To investigate the stress–strain accumulation in neighboring faults resulting from the movement across the other fault, a model of interacting strike-slip and dip-slip faults is considered in this paper. Here, both the faults are considered finite, buried and situated in a viscoelastic half-space of fractional standard linear solid medium. The analytical solutions for displacement, stress and strains are obtained in the absence of as well as after the movement of both the faults using mathematical techniques of Laplace transformation, modified Green’s function, correspondence principle and fractional derivative. Analytical results and the graphical presentations demonstrate that the velocities of the fault movement and inclinations of both faults significantly influence displacements, stresses, and strains. A comparative study has been done to understand the effect of fractional derivatives on displacement and stress–strain accumulation. These results may help to study the subsurface deformation and its effect on fault movement, causing earthquakes.</p>