Aims: We study the properties of torsional Alfvén waves in coronal loops so that they may be exploited for coronal seismological applications. Methods: The governing equation is obtained for standing torsional Alfvén waves of a dynamic, gravitationally stratified plasma. The footpoints are assumed to obey line-tying conditions necessary for standing oscillations. Solutions are found in a number of different but typical scenarios to demonstrate the possibilities for both temporal and spatial magneto-seismology exploitation of waveguides with the standing torsional Alfvén oscillations. Results: It is found that the frequency of the standing Alfvén oscillation increases as the stratification of the plasma increases. The ratio of the periods of the fundamental modeand the first overtone is also found to change as the stratification of the plasma increases. Further, the eigenfunctions of the higher overtones of the standing oscillations are found to experience a shift of their anti-nodes. The influence of a dynamic plasma on the amplitudes of the mode is also investigated. The amplitude of the torsional Alfvén mode is found to increase as the plasma within the coronal loop experiences cooling.