The Geostationary Operational Environmental Satellite R (GOES-R) series of four satellites are the next generation NOAA GOES satellites. Once on orbit and commissioned, they are renamed GOES 16–19, making critical terrestrial and space weather measurements through 2035. GOES 16 and 17 are currently on orbit, having been launched in 2016 and 2018, respectively. The GOES-R satellites include the Extreme Ultraviolet (EUV) and X-ray Irradiance Sensors (EXIS) instrument suite, which measures calibrated solar irradiance in eight lines or bands between 25 nm and 285 nm with the Extreme Ultraviolet Sensors (EUVS) instrument. EXIS also includes the X-Ray Sensor (XRS) instrument, which measures solar soft X-ray irradiance at the legacy GOES bands. The EUVS Measurements are used as inputs to the EUVS Model, a solar spectral irradiance model for space weather operations that predicts irradiance in twenty-two 5 nm wide intervals from 5 nm to 115 nm, and one 10 nm wide interval from 117 to 127 nm at 30 s cadence. Once fully operational, NOAA will distribute the EUVS Model irradiance with 1 min latency as a primary space weather data product, ushering in a new era of rapid dissemination and measurement continuity of EUV irradiance spectra. This paper describes the EUVS Model algorithms, data sources, calibration methods and associated uncertainties. Typical model (relative) uncertainties are less than ~5% for variability at time-scales longer than 6 h, and are ~25% for solar flare induced variability. The absolute uncertainties, originating from the instruments used to calibrate the EUVS Model, are ~10%. Examples of model results are presented at both sub-daily and multi-year timescales to demonstrate the model’s capabilities and limitations. Example solar flare irradiances are also modeled.