We report the discovery from the WASP survey of two exoplanetary systems, each consisting of a Jupiter-sized planet transiting an 11th magnitude (V) main-sequence star. WASP-104b orbits its star in 1.75 d, whereas WASP-106b has the fourth-longest orbital period of any planet discovered by means of transits observed from the ground, orbiting every 9.29 d. Each planet is more massive than Jupiter (WASP-104b has a mass of $1.27 pm 0.05 mathrm{M_{Jup}}$, while WASP-106b has a mass of $1.93 pm 0.08 mathrm{M_{Jup}}$). Both planets are just slightly larger than Jupiter, with radii of $1.14 pm 0.04$ and $1.09 pm 0.04 mathrm{R_{Jup}}$ for WASP-104 and WASP-106 respectively. No significant orbital eccentricity is detected in either system, and while this is not surprising in the case of the short-period WASP-104b, it is interesting in the case of WASP-106b, because many otherwise similar planets are known to have eccentric orbits.