This work investigates the effect of elastic support stiffness on the accuracy of moving load identification of Euler–Bernoulli beams. It uses the angular velocity response in solving the ill-posed inverse vibration problem and Tikhonov regularization in the load identification process of two moving loads. The effects from moving loads’ traveling direction, measurement location arrangements, number of participant measurements, and damping ratios are considered in the studies under noisy disturbance conditions. Results show that the stiffness of the translational rotational springs at the boundaries can impact the accuracy of identified moving loads considerably. Angular velocities presented much better results than accelerations under low stiffness conditions when vertical elastic supports were used. However, acceleration showed better performance when a very soft translational spring was used at one end and a much stiffer translational spring at the other end, as well as when rotational springs with large stiffness were used with simply supported beam conditions. The combination of angular velocities and accelerations provided a balanced solution for a wide range of elastic supports with different stiffnesses.