ABSTRACTWe simultaneously model the gravitational potential and phase space distribution function (DF) of giant stars near the Sun using the Gaia DR2 radial velocity catalogue. We assume that the Galaxy is in equilibrium and is symmetric about both the spin axis of the disc and the Galactic mid-plane. The potential is taken as a sum of terms that nominally represent contributions from the gas and stellar discs, the bulge, and the dark matter halo. Our model for the DF comprises two components to account for a mix of thin and thick disc stars. Each component is described by an analytic function of the energy, the spin angular momentum, and the vertical energy, in accord with Jeans theorem. We present model predictions for the radial and vertical forces within $\sim 2\, {\rm kpc}$ of the Sun, highlighting the rotation curve, the asymmetric drift curve, and the vertical force profile. We then show residuals for star counts in the R–z and z–vz planes as well as maps of the mean radial and azimuthal velocities in the z–vz plane. Using our model for the potential, we map the star count residuals in action-frequency-angle coordinates. The Gaia phase spiral, velocity arches, bending waves, and some of the known moving groups appear as well-defined features in these maps.