Methods for suppression and control of the axisymmetric vertical positional instability are described on the basis of conceptural design studies with the International Tokamak Reactor (INTOR). The shell effect is well known to be useful for suppression of the fast instability.Included in the assessments are required modellings of the plasma current for determination of mutual inductances between the plasma and the inductive components around it. Three kinds of models are described and their features are compared to the shell effect. T w o kinds of simplified reactor structures are described and studied by comparing them with some control characteristics of the slow instability by a pair of control coils. Their structures are selected so as to result in different shell effects between them, and are consequently found to produce different capacities of power supply, too.KEYWORDS: active control, axisymmetric vertical positional instability, design requirements, International Tokamak Reactor, passive control, PID controller, plasma models, shell effectHere shell structures are presented and their usefulness is assessed.