The symmetric wave modes of a two-dimensional magnetic flux sheath embedded in a compressible isothermal but nongravitational atmosphere are investigated under more general conditions than those considered earlier by Cram and Wilson. Both two-dimensional ''taut wire'' and pulsation modes are considered, and explicity solutions are obtained when the thickness of the flux sheath is small compared with the transverse scale size of the perturbations. In particular, it is found that the taut wire or Alfven-type mode may be unstable if the density within the sheath is less than that outside.The solutions for the pulsation mode are compared with those obtained by DeFouw under similar conditions. Agreement is obtained only in the limit as the sound speed in the nonmagnetic region tends to infinity. It is shown that DeFouw's analysis, which neglects all trasnverse variations in the perturbations, is unsuitable to the problem and that the approximation which he makes eliminates the interaction between the magnetic and nonmagnetic plasmas.