A toroidal, quasi-linear model is proposed to study the penetration dynamicsof the resonant magnetic perturbation (RMP) field into the plasma. The modelcouples the linear, fluid plasma response to a toroidal momentum balanceequation, which includes torques induced by both fluid electromagnetic forceand by (kinetic) neoclassical toroidal viscous force. The numerical results fora test toroidal equilibrium quantify the effects of various physical parameterson the field penetration and on the plasma rotation braking. The neoclassicaltoroidal viscous torque plays a dominant role in certain region of the plasma,for the RMP penetration problem considered in this work.
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