Even though 106Ru/106Rh applicators have been in clinical use over more than two decades for the radiotherapy of malignant uveal melanomas, the dosimetry of emitted beta radiation is still a physical problem. The dose rate at the applicator surface and the depth dose in tissue equivalent material can be determined only within +/- 30% error. Using new cubic-shaped thermoluminescence detectors (TLD) with small volume the dose distribution is examined in water equivalent material (RW-1). The spatial resolution is 14 times better compared to the previous technique. From dose measurements in an eye phantom the homogeneity of nuclide deposition and the depth dose distribution of a 106Ru/106Rh applicator are determined.