In this paper, the numerical stability of the SPH method under both tension and compression conditions are discussed by using one dimensional impact models. The artificial viscosity and the conservation smoothed approach are tried to suppress both tension and compression instability. The result clearly shows that the occurrence possibility of tension instability is much larger than the compression case. The comparison of the controlling techniques of the artificial viscous and conservation smoothed approach shows that the artificial coefficients are independent on the numerical instability but can reduce some perturbation, while the conservation smoothed approach does well for both tension and compression cases. Considering the tension instability directly , a simple method of inserting particles to avoid the numerical instability is introduced.