A strain softening model for earthquake instability on a long, vertical, strike-slip fault is analyzed using continuously distributed screw dislocations. The fault zone constitutive law is represented by a Gaussian-shaped friction law in which slip softening occurs beyond the peak stress. The peak stress varies as the Gaussian of depth, and the greatest peak stress occurs near the inferred earthquake focus. Material surrounding the fault is modeled by elastic plates with stress-free surface and bottom; forcing is by a growing displacement applied at the remote plate ends. Inertia-limited instability (an earthquake analog) occurs when the fault zone weakens with strain faster than the nearby elastic stress can decrease. Thus ratio of two stiffnesses determines if an instability will occur. Surface strain fields are less uniform for unstable cases than for stable cases.