We present an application study of the method of manufactured solutions in Lagragian code verification. We examined two sample codes, one of which is a structured grid code and the other is a unstructured grid code. We utilized the one-dimensional pure mechanical violation manufactured solution model to verify the Lagragian code of structured grid. Then we utilized the one-dimensional radiation hydrodynamics manufactured solution model to verify the Lagragian code of unstructured grid. In each case, we executed twelve steps of the code verification process of the method of manufactured solutions. The evaluation criterions include discrete error and observation precision. Simulation results of density, pressure and temperature of different grids at different times are in accord with the manufactured solutions. Observation precision of the simulation code is 2.0, which is also in accord with the theoretical precision. So the codes are verified. Results show that the method of manufactured solutions can effectively verify Lagrangian codes of both structured grid and unstructured grid.