Similarity solutions are determined for nonhomogeneous elastic semi‐infinite thin rods subjected to suddenly initiated and uniformly sustained stress at the origin. The system of governing nonhomogeneous partial differential equations along with its initial and boundary conditions is transformed to an ordinary differential equation and the corresponding auxiliary conditions by means of the similarity transformations. The representation so obtained is integrated. From the general solution of the problem, two special cases, one for the homogeneous rod and the other for the nonhomogeneous rod, are solved in closed form. The difference of behavior in two cases is graphically discussed.