If a low-power cw Ar(+) laser beam (~50 mW) is sent horizontally and focused on the entrance side of a cuvette containing an absorptive solution, the beam fans into the lower half of the cuvette instead of propagating through and forming self-phase-modulation fringes. We call this phenomenon self-beam fanning, which has been observed in several organic solutions. We present here several experimental results and a descriptive model of the phenomenon.