In order to more accurately describe the seepage characteristics of shale gas reservoirs, in this paper, an elastic outer boundary condition is introduced, and a new dual-media shale gas seepage model is established to describe the seepage characteristics of shale gas reservoirs more accurately, while considering the adsorption and desorption process. Combining Laplace transformation and Similar Structure Method, the solution of the percolation model is obtained in Laplace space. Furthermore, the solutions are inverted into real space with the Stehfest numerical inversion method. Type curves of dimensionless pressure and dimensionless pressure derivative can be used to evaluate the reservoir characteristics. The results show that the conventional three kinds of outer boundary conditions (infinite, constant pressure and closed) are actually three special cases of elastic outer boundary. The introduction of elastic outer boundary conditions not only expands the scope of data interpretation, but also closer to the actual situation of the outer boundary of the reservoir. The theory of similar structure greatly simplifies the complex process of solving the model and will have a far-reaching impact on the development of well test analysis software in the future.