Abstract: With the development and readiness of inter-satellite link (ISL), it has been widely used in satellite constellations for navigation, communication and other purposes. As establishing or maintaining ISL can be affected by transits (also known as sun outage), transits of the links need to be calculated and predicted, so the system service can be properly assessed and scheduled. Currently the normal practice to determine and predict the transits, by building scenarios using proven commercial satellite system toolkit or by developing in-house simulation tools, is to calculate the elongation between the ISL and the line-of-sight of the Sun, based on propagated ephemerides. It is simple, straight forward and can be conveniently implemented, however, it bears a significant disadvantage that the computation is extremely CPU-intensive and therefore slow in speed. Although the predicted transits do not have to be very precise in the design phase and the two-body model may suffice, the ephemerides are always limited to small stepsize in order to properly detect the transits. Otherwise transits with short duration may be overlooked and the service assessment can be compromised. Regarding the determination and calculation of the transits, a fast algorithm is proposed in this paper. With the equation of the satellite's argument of latitude u at the transit boundary, it can be analytically determined whether a transit may occur or calculated when the transit starts or ends, allowing fast assessment of how transits affect the service. This method is also based on propagated ephemerides, but a much larger stepsize can be accepted. Tests show that the analytical method can outperform the normal practice by detecting more transits while reducing calculation time by two to three orders of magnitude. Even the stepsize of the ephemerides is close to one orbital period, this method is still able to detect more than 99.9% transits. The results are robust against varying stepsizes, where the maximum deviations of calculated onset epochs and durations of the transits would not exceed 1 second.