Crack detection of critical beam structures such as bridges and aircraft wings by vibration monitoring is based on understanding how a crack affects the vibration characteristics of a beam structure. Transfer matrix method is a convenient, effective, and hence widely used approach to beam vibration analysis, but a crack in the beam makes this method ineffective. This paper proposes an open crack model that simulates the local stiffness reduction effect of a transverse crack by a rectangular slot to make the transfer matrix method able to analyze vibrations of a cracked beam. The depth of the slot is identical to the depth of the crack, and the equivalent width of the slot is obtained by comparison of stiffness reductions of finite element analysis results and the counterpart transfer matrix method results. Different dimensions of rectangular beams, different crack positions and loading conditions are considered and statistic method is used to improve the generality and accuracy of the model. A calculation example of a cracked cantilever beam is given and the validity of the proposed model is verified with available results of existing models.