The formulation of Smoothed Particle Hydrodynamics (SPH) and a shortcoming of traditional SPH in contact simulation are presented. A contact algorithm is proposed to treat contact phenomenon between two objects. We describe the boundary of the objects with non-mass artificial particles and set vectors normal to the contact surface. Contact criterion using non-mass particles is established in this study. In order to verify the contact algorithm, an algorithm is implemented in to an in-house program; elastic wave propagation is an analysed under low velocity axial impact of two rods. The results show that the contact algorithm eliminates the undesirable phenomena at the contact surface; numerical result with the contact algorithm is compared with theoretical one.