We investigate the regularity of cluster pressure profiles with REXCESS, a representative sample of 33 local (z < 0.2) clusters drawn from the REFLEX catalogue and observed with XMM-Newton. The sample spans a mass range of 1014 M < M500 < 1015 M , where M500 is the mass corresponding to a density contrast of 500. We derive an average profile from observations scaled by mass and redshift according to the standard self-similar model, and find that the dispersion about the mean is remarkably low, at less than 30 per cent beyond 0.2 R500, but increases towards the center. Deviations about the mean are related to both the mass and the thermo-dynamical state of the cluster. Morphologically disturbed systems have systematically shallower profiles while cooling core systems are more concentrated. The scaled profiles exhibit a residual mass dependence with a slope of ∼0.12, consistent with that expected from the empirically-derived slope of the M500 − YX relation; however, the departure from standard scaling decreases with radius and is consistent with zero at R500. The scatter in the core and departure from self-similar mass scaling is smaller compared to that of the entropy profiles, showing that the pressure is the quantity least affected by dynamical history and non-gravitational physics. Comparison with scaled data from several state of the art numerical simulations shows good agreement outside the core. Combining the observational data in the radial range [0.03−1] R500 with simulation data in the radial range [1−4] R500, we derive a robust measure of the universal pressure profile, that, in an analytical form, defines the physical pressure profile of clusters as a function of mass and redshift up to the cluster “boundary”. Using this profile and direct spherical integration of the observed pressure profiles, we estimate the integrated Compton parameter Y and investigate its scaling with M500 and LX, the soft band X-ray luminosity. We consider both the spherically integrated quantity, Ysph(R), proportional to the gas thermal energy, and the cylindrically integrated quantity, Ycyl(R) = YSZDA, which is directly related to the Sunyaev-Zel’dovich (SZ) effect signal. From the low scatter of the observed Ysph(R500)−YX relation we show that variations in pressure profile shape do not introduce extra scatter into the Ysph(R500)−M500 relation as compared to that from the YX−M500 relation. The Ysph(R500)−M500 and Ysph(R500)−LX relations derived from the data are in excellent agreement with those expected from the universal profile. This profile is used to derive the expected YSZ − M500 and YSZ − LX relations for any aperture.