We present the first galactic-scale model of the gas dynamics of the prototype barred Seyfert 1 galaxy NGC 1097. We use large-scale FaNTOmM Fabry-Perot interferometric data covering the entire galactic disc and combine the distribution and kinematics maps with high-resolution two-dimensional spectroscopy from the Gemini telescope. We build a dynamical model for the gravitational potential by applying the analytic solution to the equations of motion, within the epicyclic approximation. Our model reproduces all the significant kinematic and structural signatures of this galaxy. We find that the primary bar is 7.9 ± 0.6 kpc long and has a pattern speed of 36 ± 2 km s-1 kpc-1. This places the corotation radius at 8.6 ± 0.5 kpc, the outer Lindblad resonance at 14.9 ± 0.9 kpc and two inner Lindblad resonances at 60 ± 5 pc and 2.9 ± 0.1 kpc. These derivations lead to a ratio of the corotation radius over bar length of 1.0-1.2, which is in agreement with the predictions of simulations for fast galaxy bars. Our model presents evidence that the circumnuclear ring in this galaxy is not located near any of the resonance radii in this galaxy. The ring might have once formed at the outer inner Lindblad resonance radius, and it has been migrating inwards, towards the centre of the galactic gravitational potential.