We present a new model for the gas dynamics in the galactic disc inside the orbit of the Sun. Quasi-equilibrium flow solutions are determined in the gravitational potential of the deprojected COBE near-infrared bar and disc, complemented by a central cusp and, in some models, an outer halo. These models generically lead to four-armed spiral structure between corotation of the bar and the solar circle; their large-scale morphology is not sensitive to the precise value of the pattern speed of the bar, to the orientation of the bar with respect tc, the observer, or to whether or not the spiral arms carry mass. Our best model provides a coherent interpretation of many observed gas dynamical features. Its four-armed spiral structure outside corotation reproduces quantitatively the directions to the live main spiral arm tangents at \l\ less than or equal to 60 degrees observed in a variety of tracers. The 3-kpc arm is identified with one of the model arms emanating fi om the ends of the bar, extending into the corotation region. The model features an inner gas disc with a cusped orbit shock transition to an x(2) orbit disc of radius R similar to 150 pc. The corotation radius of the bar is fairly well constrained at R(c) similar or equal to 3.5 +/- 0.5 kpc, The best value for the orientation angle of the bar is probably 20-25 degrees, but the uncertainty is large since no detailed quantitative fit to all features in the observed (l, v) diagrams is yet possible. The Galactic terminal velocity curve from H I and CO observations out to l similar or equal to +/-45 degrees (similar to 5 kpc) is approximately described by a maximal disc model with constant mass-to-light ratio for the near-infrared bulge and disc.