Accurate description of induced gas flow in an unsaturated zone is indispensable for characterizing the unsaturated zone. Hantush's approximation and a finite difference approximation of the leakage term are frequently employed in modeling the induced gas flow in an unsaturated zone underlying a leaky confining layer. However, no studies have been conducted on the errors that result from these approximations. This study presents a physically more rigorous model based on mass conservation in both the upper leaky confining layer and the lower permeable layer (the unsaturated zone). Flow in the upper layer is assumed to be vertical, and in the lower layer, it is two-dimensionally axisymmetric, with gas pressure and flux continuity at the interface of the two layers. A new steady state solution for a well with a finite radius and two new transient solutions for a well with an infinitely small radius and with a finite radius are developed for this rigorous model. In addition, another new transient solution is derived using the finite difference approximation of the leakage term for the same problem. The developed solutions are compared with previous approximate solutions. Results indicate that Hantush's approximation overestimates the gas pressure at shallower depths and underestimates it at deeper depths under the condition of gas injection. This error changes with the hydrogeological parameters and well configurations. The finite difference approximation works reasonably well under the usual field conditions. Neglecting the well radius for a small radius well does not induce much error.