We present an analysis of the far-infrared and submillimetre molecular emission line spectrum of the luminous M-supergiant VY CMa, observed with the SPIRE and PACS spectrometers aboard the Herschel Space Observatory. Over 260 emission lines were detected in the 190-650-micron SPIRE FTS spectra, with one-third of the observed lines being attributable to H2O. Other detected species include CO, 13CO, H2^18O, SiO, HCN, SO, SO2, CS, H2S, and NH3. Our model fits to the observed 12CO and 13CO line intensities yield a 12C/13C ratio of 5.6+-1.8, consistent with measurements of this ratio for other M supergiants, but significantly lower than previously estimated for VY CMa from observations of lower-J lines. The spectral line energy distribution for twenty SiO rotational lines shows two temperature components: a hot component at 1000 K, which we attribute to the stellar atmosphere and inner wind, plus a cooler ~200 K component, which we attribute to an origin in the outer circumstellar envelope. We fit the line fluxes of 12CO, 13CO, H2O and SiO, using the SMMOL non-LTE line transfer code, with a mass-loss rate of 1.85x10^-4 Msun yr^-1 between 9 R* and 350 R*. To fit the observed line fluxes of 12CO, 13CO, H2O and SiO with SMMOL non-LTE line radiative transfer code, along with a mass-loss rate of 1.85x10^-4 Msun yr^-1. To fit the high rotational lines of CO and H2O, the model required a rather flat temperature distribution inside the dust condensation radius, attributed to the high H2O opacity. Beyond the dust condensation radius the gas temperature is fitted best by an r^-0.5 radial dependence, consistent with the coolant lines becoming optically thin. Our H2O emission line fits are consistent with an ortho:para ratio of 3 in the outflow.
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