This paper analyzes the effect of tire/vehicle parameters, specifically of tire/suspension torsional stiffnesses, on the stability of self-excited tire torsional oscillations during locked-wheel braking events. Using a torsionally flexible tire-wheel model and a dynamic tire-ground friction model, two system models for tire oscillations are considered: with suspension torsional compliance included in one but excluded in the other. Bifurcation analysis is conducted on both systems to derive the effect of tire/vehicle parameters on the stability. For the system without suspension torsional compliance, it is highlighted that the primary cause of unstable self-excited oscillations is the “Stribeck” effect in tire-ground friction. Based on the parameters obtained experimentally, the bifurcation surface of vehicle velocity with respect to tire/suspension torsional stiffness is also given. The effect of tire/suspension torsional stiffness to the stability of tire torsional oscillation is qualitatively validated via comparisons between locked-wheel braking simulations and experiments with tires with different torsional stiffnesses.