The derivation of the shape factor in analytical models for flow in double-porosity media is often partially empirical. This study proposes a new flow equation and shape factor for matrix domains, eliminating empirical derivations in the context of a standard pumping test in double-porosity confined aquifers. For a single-fracture strip matrix medium, a new analytical model incorporating the proposed flow equation and shape factor was developed, and its analytical solution was derived. For a fracture-network matrix medium, a finite element solution was constructed based on the new flow equation and shape factor, without discretizing individual matrix spaces. The results indicate that the shape factor for the strip matrix is the reciprocal of the square of the matrix width, whereas for a circular matrix, it is the reciprocal of the square of the radius. However, for other matrix shapes, it remains an empirical parameter. The relative error in fracture drawdown predicted by the analytical solution incorporating the new shape factor is less than 5%, whereas existing shape factors yield a relative error of approximately 99%. When the ratio of fracture area to total medium area (defined as fracture density) exceeds 62%, the fracture-network matrix medium can be considered a double-porosity continuous medium. The finite element solution was applied to a field standard pumping test, demonstrating its effectiveness.