This paper describes the implementation of Classical Trajectory Calculation Direct Simulation Monte Carlo (CTC-DSMC) for one dimensional shock waves in molecular nitrogen including rotational-vibrational excitation. It is demonstrated that CTC-DSMC and Molecular Dynamics simulations agree exactly for the translational, rotational, and vibrational temperature profiles within a one dimensional shock. By comparing various shocks with the harmonic oscillator and anharmonic oscillator potentials it is found that ro-vibrational coupling increases with the degree of anharmonicity. For relevant shock wave conditions for high-speed, high-altitude flight, the overshoot in rotational temperature behind the shocks is decreased, while vibrational excitation rate is increased. This reduction in rotational temperature overshoot and increase in vibrational relaxation rate were found to become more pronounced as the post shock temperature increases. Additionally, CTC- DSMC simulations of reflected shock waves are verified with simulations of standing shock waves.