Abstract: The influence of the cylindrical plasma pressure and viscosity on the axial eigen-function was analytically described in the linearized ideal magneto-hydrodynamic equations and numerically solved in semi-classical method.The calculated results included:ⅰ) The axial eigenfunction decreases with an increase of the plasma pressure and is little affected by the plasma viscosity, suggesting a positive impact of a uniform plasma pressure on themacroscopic plasma stability;ⅱ) The axial eigenfunctions are negative (positive) when the plasma radii are smaller (greater) than 0.3;and ⅲ) At a low plasma pressure and in the vicinity of thecylindrical axis and/or near the plasma wall, the viscosity significantly affects the axial eigenfunction.