Active gas control systems are commonly used in municipal solid waste (MSW) landfills and the design of such systems requires thorough understanding of the gas flow pattern. A model is developed to predict the two-dimensional radial transient gas flow to a vertical gas extraction well in deformable MSW landfills. Variations of gas storage include time-dependent compression of the refuse, dissolution of gas components and porosity enlargement due to organic matter degradation. Mechanical compression of solid skeleton is coupled with gas pressure using K-H rheological model which is capable of reproduce the evolution of settlement for MSW landfills. The new analytical solution obtained in Laplace transform domain can be used to determine excess gas pressure fields, gas fluxes in the well and through the top cover as well as landfill settlements. The solution is validated by comparison with field measurements and numerical simulations. It demonstrates that the gas storage variation term becomes predominant only during early times. Long-term gas flow is controlled by the gas generation rate and the quasi-steady solution is valid. Parametric studies indicate that the solution given in this paper is useful for the prediction of gas fluxes, for the choice of the optimum spacing between wells, and for the determination of the final cover properties as well as appropriate vacuum pressure imposed in the extraction well.