An expression for the compressibility ▽·ξ of a plasma is obtained from the linearized magnetohydrodynamic equations of motion. This compressibility term, in general, consists of two different parts: the first connects with the longitudinal initial motion of the plasma, and the second with the uniform motion (dilatation and contraction) of the plasma-carrying magnetic tubes. For a plasma column, several cases are considered which permit us to simplify to some extent the solution of the equation of motion including the compressibility term. With the aid of these results, a dispersion relation describing the motion of the plasma column with uniform current distribution is derived and analysed.