For a highway bridge subjected to a moving mass, it was shown that the frequency of a moving mass-bridge system changes with time in reality. However, this phenomenon was seldom discussed in the literature and requires further investigation from the practical point of view. As such, this study first derives the analytical formulation to illustrate the frequency variation in a moving mass-beam system and then extends to derive the semi-analytical solutions of a moving mass-plate system; in addition, the three-dimensional models are established accordingly to numerically investigate the effects of moving mass on civil structures. From the numerical results, it is shown that the instantaneous frequency ratios of the first three modes can reach more than 10% for a moving mass-beam system with high suspension stiffness and large vehicle-to-bridge mass ratio, and the frequency variation for the first mode can reach 20% for a plate-type bridge. By comparison, it is noticed that the wave propagation is uniquely exhibited in the acceleration responses of a plate-type bridge, while this phenomenon is uncommon for a beam-type bridge.