Based on Euler-Bernoulli beam and structure dynamics theory and by means of numerical experimentation, taking a single-damaged simply supported beam as the research object, this paper obtains the frequencies of the beam under the conditions of different damage positions and damage degrees. With the concept of damage factor, rate of change of frequency(RCF), mean value of RCF(MRCF), amplitude of RCF(ARCF), and the ratio of RCF(RRCF), the paper researches frequency characteristics of a simply supported beam. The results show that the frequency and RCF sensitivities are related to damage degree and damage position, and that the RRCF sensitivities are relate to damage position only. The influence of damage degree on the frequency is greater than that of damage position, and that the RCF value variation of the beam is not a monotonic function with the increase of modal order when the damage position and damage degree are constant. The frequency and RCF of the beam at different damage position are oscillation curves, and the oscillation times and amplitude value of RCF curve varies with the change of modal order.