An analytic stationary solution for rotating, magnetized, non-self-gravitating filamentary molecular clouds is presented as a model for molecular tornadoes. This model results in monotonically decreasing density profiles for rotating filaments, unlike previous filament models, which suffered radial oscillations in density referred to as density inversions. Whereas previous models consider the effect of self-gravity on molecular clouds, we use estimates derived from observations of the Double Helix Nebula, the Galactic Centre Tornado, and the Pigtail Nebula in the Central Molecular Zone of the Milky Way Galaxy that highly pressure truncated filamentary clouds are at most weakly self-gravitating. The simulation code Athena++ is used to study the time evolution of the model to assess its stability and evolution. Two different sets of boundary conditions are simulated, one which simulates an infinitely long idealized filament and another which simulates a finite filament protruding from a fixed rotating source. Simulations of the model do not develop detectable instabilities until at least twenty-five sound crossing times. However, simulations seeded with white noise with a standard deviation 0.01 in their initial density profiles develop kink instabilities within ten sound crossing times