Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis. For any given initial data with two pieces of constant states, the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states, the solution may be constructed from the Riemann solutions, with each two adjacent states connected by elementary waves. A new Riemann problem forms when these two waves collide. Through the exploration of these Riemann problems, the outcome of wave interactions may be classified in a suitable parametric space.