Abstract: The stability of one dimensional standard SPH with a cubic B-spline kernel isanalyzed by von Neumann stability analysis method, and the effect ofperturbation wavelength on the stability of SPH is discussed. The results oftheoretical analysis are verified by numerical SPH computations of aone dimensional elastic bar, in which different wavelength perturbationare applied on the SPH particles. The numerical test indicates that the SPHstability is closely related with the perturbation wavelength. The numericalstable domain shape is the same as that of theoretical analysis exceptan offset of thestable domain boundaries of the numerical test. The SPHmethod used in this paper is the most unstable at the shortestperturbation wavelength, and it can bestable in tension at other perturbation wavelengths.