Assuming that the flow of matrix to the fractures is a proposed steady state flow, a two-dimensional box-type formation horizontal well model with fluid supply from the fractures to the wellbore and the existence of matrix to fracture flow and cavern to fracture flow is established, and two kinds of boundary conditions in the top-bottom direction (Constant-pressure boundary, impermeable boundary) and three kinds of boundary conditions in the vertical wellbore direction (Constant-pressure boundary, impermeable boundary, Infinite boundary) are taken into account. The boundary value problem is transformed into the Laplace domain using Fourier cosine and Laplace transforms. Through the similarity construction method incorporating wellbore storage and skin effects, a unified continuous fractional solution for bottomhole pressure is derived. Finally, the solution is inverted into real space by the Stehfest numerical inversion method, and a double logarithmic plate is plotted for sensitivity analysis. For the first time, the similarity construction method is introduced into the solution of two-dimensional box-type horizontal well model with triple media, which can simplify the algorithm and improve the efficiency.