Assuming that the solar activity and the solar cycle phenomena may be manifestations of global torsional MHD oscillations, we compute the Alfven wave travel times along the field lines in the five models of magnetic field described in the following text. For all these models, we compute standard deviation and it's ratio to mean Alfvenic wave travel times. The last two models yield the smallest relative bandwidth for the frequencies of the MHD oscillations. However, the last model is the only admissible one which can sustain global Alfvenic oscillations with well defined frequency for the fundamental mode