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SUMMARY This paper examines the linear stability of sliding on faults embedded in a 2-D elastic medium that obey rate and state friction and have a finite length and/or are near a traction-free surface. Results are obtained using a numerical technique that allows for analysis of systems with geometrical complexity and heterogeneous material properties; however only systems with homogeneous frictional and material properties are examined. Some analytical results are also obtained for the special case of a fault that is parallel to a traction-free surface. For velocity-weakening faults with finite length, there is a critical fault length $$L^{*}$$ for unstable sliding that is analogous to the critical wavelength $$h^{*}$$ that is usually derived from infinite fault systems. Faults longer than $$L^{*}$$ are linearly unstable to perturbations of any length. On vertical strike-slip faults or faults in a full-space $$L^{*} \approx h^{*}/e$$, where e is Euler’s number. For dip-slip faults near a traction-free surface $$L^{*} \le h^{*}/e$$ and is a function of dip angle $$\beta$$, burial depth d of the fault’s up-dip edge and friction coefficient. In particular, $$L^{*}$$ is at least an order of magnitude smaller than $$h^{*}$$ on shallowly dipping ($$\beta < 10^\circ$$) faults that intersect the traction-free surface. Additionally, $$L^{*} \approx h^{*}/e$$ on dip-slip faults with burial depths $$d \ge h^{*}$$. For sliding systems that can be treated as a thin layer, such as landslides, glaciers or ice streams, $$L^{*} = h^{*}/2$$. Finally, conditions are established for unstable sliding on infinitely-long, velocity-strengthening faults that are parallel to a traction-free surface.