The collisional probability of short-period (SP) comets with Jupiter was estimated from numerical integrations of the orbits of real 165 SP comets over 4400 years. The cumulative close-encounter distance vs frequency plot was extrapolated to the radius of Jupiter taking account of the gravitational focusing effects in order to obtain the mean collisional probability. The obtained value gave a fairly good agreement with that calculated by D. Olsson-Steel (1987, Mon. Not. R. Astron. Soc. 227, 501-524) based on a form of Öpik's method. Incorporating the estimated flux of invisible SP comets near the Jovian orbit in the observed range of H 10-magnitude, the intrinsic collision rate with Jupiter was found to be once per 950 years, which is nearly 15 times more frequent than the collision rate for long-period comets calculated by Olsson-Steel (1987). The total impact numbers of comets with each jovian satellite over the Solar System age were calculated for the steady-state flux model of comets. It is shown that the surface densities of ray-craters (youngest) on Ganymede and Callisto ( D gt; 30 km) are in agreement, within a factor of two, with our calculated intrinsic flux of SP comets. From the fact that the number of large craters on Amalthea (JV) is nearly equal to the total impact number predicted from the steady-state flux of comets, it is proposed that Amalthea may be the remnant core of a larger parent body whose original surface was spalled by many catastrophic impacts, or it may be a new object recently captured into the present orbit. We also suggest that the maximum size of craters on the retrograde outer satellites, which could be measured by the Galileo spacecraft, be a good tester for the knowledge of the cometary flux integrated over 4.6 × 10 9 years near the orbit of Jupiter. It is discussed that current survival of some inner small satellites might give a clue to the upper limit of the integrated cometary flux there.