The paper aims to construct a theoretical model on locally resonant phononic crystal beams with boundary conditions. In the model， a simply supported beam is attached to periodic spring-mass systems. In terms of the Hamilton's principle， the dynamic equation of the model is formulated in theory. Further， the dynamic characteristics and locally resonant band gaps of the model are achieved by using the Rayleigh-Ritz method. The numerical results agree well with the experimental data in the previous literature， indicating that the presented model is feasible in theory. According to the presented model， band gaps of the phononic crystal beams considering different beam lengths and lattice constants are investigated. When the lattice constant of the periodic structure is smaller than the beam length， band gaps in frequency response curves are distinctly observed. Besides， there are anti-resonant crests located in the band gaps which correspond to the natural frequency of a spring-mass system. On the other hand， the band gaps are complicated and heavily influenced by the boundary condition if the lattice constant increases.