The Magnetohydrodynamic stability of a streaming cylindrical model penetrated by varying\ntransverse magnetic field has been discussed. The problem is formulated, the basic equations are\nsolved, upon appropriate boundary conditions the eigenvalue relation is derived and discussed\nanalytically, and the results are verified numerically. The capillary force is destabilizing in a small\naxisymmetric domain 0 < x < 1 and stabilizing otherwise. The streaming has a strong destabilizing\neffect in all kinds of perturbation. The toroidal varying magnetic field interior the fluid has no\ndirect effect at all on the stability of the fluid column. The axial exterior field has strong stabilizing\neffect on the model. The effect of all acting forces altogether could be identified via the numerical\nanalysis of the stability theory of the present model.
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