A dynamic model of echinococcosis in livestock, domestic dogs, stray dogs and eggs in the environment is established, and the influence of stray dogs on the transmission of echinococcosis is discussed. Firstly, by using the fundamental theorem of differential equation, the adaptability of the model solution is obtained, including non-negative and boundedness. Secondly, the equilibrium point and the basic regeneration number of the model are obtained. By analyzing the characteristic equation and the Lyapunov function, it is obtained that when the basic regeneration number is less than 1, the disease-free equilibrium point is asymptotically stable, namely, the echinococcosis tends to be extinct. When the basic regeneration number is greater than 1, the disease-free equilibrium point is unstable, and the endemic equilibrium point is asymptotically stable, namely, the echinococcosis persists.