The vibrational stability of detailed models of Cephei stars is studied by numerical integration of the linearized non-adiabatic pulsation equations. In contrast to a previous investigation, improvements in the method of integration allow the non-adiabatic calculations to be carried from the surface layers deep into the star. The periods are also determined from the models. It is found that both the period and the stability coefficient can be evaluated to high accuracy on the basis of the outer half (in mass) of the star. The effect of convection on the structure of the equilibrium models is included; the interaction of convection with the pulsations is neglected. Boundary conditions are discussed in detail in an appendix. A series of fifteen models of 7 Mo lying along a portion of the evolutionary track calculated by Hofmeister, Kippenhahn, and Weigert has been investigated. The results confirm the existence of a region of linear instability, due largely to the destabilizing effect of second helium ionization, in a range of mean effective temperatures centered at about 5400 K. The instability is present for both the fundamental mode and the first overtone. In contrast to previous work, the hydrogen and first helium ionizations are found to contribute significantly to the destabilizing effect, especially for the overtones. The instability zone is wider in terms of effective temperature than is indicated by observations, and the temperatures of the most unstable models appear to be several hundred degrees lower than the observed temperatures of Cephei stars. The results are consistent with those of our previous work and of Cox. Possible consequences of the neglect of non-linear effects are discussed in a general way. The importance of the investigation of Cepheid pulsation as a check on the correctness of models for the evolution and structure of late-type stars in the helium-burning stages of evolution is pointed out.