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Elliptical flow exists in the near vertical fracture area, or in anisotropic reservoirs, and the classical radial flow models cannot provide complete analysis for elliptical flow. This paper presents a mathematic model for gas elliptical flow in double porosity gas reservoirs. The differential equation of gas flow is written in Mathieu equation, so that the solution can be expressed also by Mathieu functions. The numerical calculation of relevant Mathieu functions , and its derivative is done to obtain the dimensionless pseudo pressure drop in Laplace space. Property sensitivities of double porosity systems including combination of , parameter related to anisotropy, storativity ratio , interporosity flow coefficient are studied by using the Laplace numerical inversion. The new solution not only includes factors considered for classic solutions in previous papers, but also incorporates the effect of reservoir anisotropy. It is kind of modification and supplementation to classic solutions.