The nuclear stellar disc (NSD) is a flattened high-density stellar structure that dominates the gravitational field of the Milky Way at Galactocentric radius 30 pc less than or similar to R less than or similar to 300 pc. We construct axisymmetric self-consistent equilibrium dynamical models of the NSD in which the distribution function is an analytic function of the action variables. We fit the models to the normalized kinematic distributions (line-of-sight velocities + VIRAC2 proper motions) of stars in the NSD survey of Fritz et al., taking the foreground contamination due to the Galactic Bar explicitly into account using an N-body model. The posterior marginalized probability distributions give a total mass of M-NSD = 10.5(-1.0)(+1.1) x 10(8) M-circle dot, roughly exponential radial and vertical scale lengths of R-disc = 88.6(-6.9)(+9.2) pc and H-disc = 28.4(-5.5)(+5.5) pc, respectively, and a velocity dispersion sigma similar or equal to 70 km s(-1) that decreases with radius. We find that the assumption that the NSD is axisymmetric provides a good representation of the data. We quantify contamination from the Galactic Bar in the sample, which is substantial in most observed fields. Our models provide the full 6D (position + velocity) distribution function of the NSD, which can be used to generate predictions for future surveys. We make the models publicly available as part of the software package AGAMA.