We consider standing wave solutions of the linearized magnetohydrodynamic (MHD) equations describing a perfectly conducting but viscous magnetofluid in a gravitationally-stratified cylindrical plasma. We assume a relatively strong homogeneous background magnetic field within the flux tube, which is oriented along the cylinder axis; the background atmosphere is in hydrostatic equilibrium, with gravity uniform and parallel to the cylinder axis; the vertical temperature profile (constrained by the stability conditions) is arbitrary. The MHD wave equations are separable, and appropriate boundary conditions are formulated. We employ a numerical shooting scheme to solve the coupled ordinary differential equations and to obtain the damping rates and eigenfrequency spectra for the standing MHD wave modes. Three series of modes are obtained for an isothermal flux tube: Alfvtnic, quasi-fast, and quasi-slow. The quasi-slow mode series is novel, having been missed previously. In the inviscid limit, with a strongly stratified atmosphere, we use three approximate characteristic dispersion relations to reveal the physical nature of the three MHD eigenmode series. The relevance of the present investigation to umbral oscillations in sunspots is briefly discussed.