This paper presents a systematic design and training procedure for the feed-forward back-propagation neural network (NN) modeling of both forward and inverse behavior of a rotary magnetorheological (MR) damper based on experimental data. For the forward damper model, with damper force as output, an optimization procedure demonstrates accurate training of the NN architecture with only current and velocity as input states. For the inverse damper model, with current as output, the absolute value of velocity and force are used as input states to avoid negative current spikes when tracking a desired damper force. The forward and inverse damper models are trained and validated experimentally, combining a limited number of harmonic displacement records, and constant and half-sinusoidal current records. In general the validation shows accurate results for both forward and inverse damper models, where the observed modeling errors for the inverse model can be related to knocking effects in the measured force due to the bearing plays between hydraulic piston and MR damper rod. Finally, the validated models are used to emulate pure viscous damping. Comparison of numerical and experimental results demonstrates good agreement in the post-yield region of the MR damper, while the main error of the inverse NN occurs in the pre-yield region where the inverse NN overestimates the current to track the desired viscous force.