This paper reports a linear temporal instability analysis of an incompressible plane gas sheet in a quiescent viscous liquid medium of infinite expanse. Results indicate that there exist two unstable modes of disturbance waves, sinuous and varicose, and surface tension always reduces, while the relative velocity between the gas and liquid phases and the gas density always enhance instability development. For both unstable modes, the presence of liquid viscosity increases the instability limit, which is however independent of the absolute value of viscosity. It is also shown that the sinuous mode becomes stable when the gas Weber number, defined as the ratio of aerodynamic forces to surface tension forces, is less than the critical value of one. At slightly larger gas Weber numbers, liquid viscosity exhibits dual effects—it may enhance or suppress the growth of unstable disturbances, depending on specific flow conditions. However, for sinuous mode at high Weber numbers and varicose mode at any Weber numbers, liquid viscosity always reduces disturbance growth rates and dominant wave numbers. Unlike the case for plane liquid sheets, varicose mode controls the instability process for all Weber number ranges and for both inviscid and viscous liquids, and only at high Weber numbers, do varicose and sinuous modes become almost equally important. It is further found that the wave propagation velocity for both unstable modes is much smaller than the gas velocity at the mode of maximum instability, implying that the disturbance waves appear almost stationary rather than travelling‐wave type, in contrast with the plane liquid sheet results. ©1996 American Institute of Physics.