For the problem of sand erosion from the side walls of punctured geotubes, a set of experimental apparatus was developed to study the erosion stability along seams between tubes of a punctured geotube dam. Based on the experiments in both unidirectional flow and wave flow conditions, characteristics of erosion process and sand transport in the seams between geotubes were summarized. The impact of breakage on the scouring stability in unidirectional flow conditions was also analyzed. The results show that scouring stability in the seams between geotubes in unidirectional flow conditions is related to the threshold velocity of the sand particles with the maximum diameter, velocity magnitudes inside the seam and the extent of the breakage. Scouring instability can easily occur in the case of larger breakage, higher flow velocity and lower threshold velocity of sand particles. In wave flow conditions, the critical peak water pressure is selected as a criterion parameter to determine the stability of seams between punctured geotubes. The scouring stability in wave flow conditions for real engineering works can be determined by comparing the peak water pressure in the seams with the critical value.