The spectrum of X rays from the planet Jupiter is calculated according to an auroral electron beam model. The electrons are assumed to be accelerated by a field-aligned potential drop and penetrate into the atmosphere as a Maxwellian beam of primaries which are scattered, degraded in energy, and merged with a population of ionization secondaries having a power law energy distribution. The soft X rays observed by the Einstein Observatory satellite are due to bremsstrahlung from the secondary electrons in the H2 atmosphere. A good match to the X ray data is obtained if the power law spectral index of the secondary electrons, &ggr;e, is ≂2, yielding a power law slope for the photon flux &ggr;X=&ggr;e+1≂3. The X ray intensity is best reconciled with a beam of primaries having a characteristic energy 30--100 keV and penetrating the homopause with an auroral energy flux typically of 10--20 ergs cm-2 s-1 but no greater than 50 ergs cm-2 s-1. ¿ American Geophysical Union 1990