We describe the operation of an all solid-state pulsed dye laser of high repetition rate (10 kHz) pumped by a diode-pumped laser. Three different active media in the form of coin-sized disks were investigated: the dye rhodamine 6G doped in a copolymer of methyl methacrylate (MMA) and 2-hydroxyethyl methacrylate (HEMA) [Rh6G/P(MMA:HEMA)], and the dye pyrromethene 567 (PM567) doped in copolymers of MMA with pentaerythritol triacrylate (PETA) and with pentaerythritol tetraacrylate (PETRA) [PM567/P(MMA:PETA) and PM567/P(MMA:PETRA)]. Pump radiation at 527nm was provided by a frequency-doubled diode-pumped Nd:YLF laser Q-switched at 10 kHz. Laser output was observed with an initial average power of 560 mW for Rh6G in P(MMA:HEMA), and with an initial average power of 430 mW for PM567 in P(MMA:PETRA) and 220 mW for PM567 in P(MMA:PETA). In the case of Rh6G/P(MMA:HEMA), the output decreased to about half the initial value after about 6.6 min (or about 4.0 million shots) due to dye degradation. The device constitutes a tunable, all solid-state, high repetition rate laser system possibly suitable for biomedical and dermatological applications.