As one of the important non-destructive testing techniques for evaluating material performance degradation and stress state, magnetic Barkhausen noise (MBN) has broad application prospects. Clarifying the relationship between internal stress distribution and detection signal can provide important guidance for evaluating the stress state of material based on the MBN signal. In this work, by constructing the expression of Barkhausen noise excitation intensity related to stress value, combining with the signal attenuation effect during signal propagation, and using the layered model along the thickness direction, we establish the analytical model of MBN signal on the surface of the ferromagnetic plate with internal stress distribution. Based on the existing experimental results, it is confirmed that the proposed model can reflect the effects of the different uniform stresses in the ferromagnetic plate on the signal at different detection frequencies. For the ferromagnetic plate with internal stress distribution, the effects of its stress distribution, magnetic conductivity, electrical resistivity, and thickness on the surface MBN signal are discussed in detail based on the proposed model. The theoretical analysis in this work can be applied to the testing mechanism analysis of the MBN stress evaluation method.