In several applications, data objects are assumed to move on predefined spatial networks such as road segments, railways, invisible air routes. Moving objects may exhibit similarity with respect to their traversed paths, and therefore two objects can be correlated based on their path similarity. In this paper, we study similarity search for moving object trajectories for spatial networks. The problem poses some important challenges, since it is quite different from the case where objects are allowed to move without any motion restrictions. Experimental results performed on real-life spatial networks show that trajectory similarity can be supported in an effective and efficient manner, by using metric-based access methods.