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We describe the implementation of the Smoothed Particle Hydrodynamics (SPH) method on graphical processing units (GPU) using the Compute Unified Device Architecture (CUDA) developed by NVIDIA. The entire algorithm is executed on the GPU, fully exploiting its computational power. The code vfaces all three main components of an SPH simulation: neighbor list constructions, force computation, integration of the equation of motion. The simulation speed achieved is one to two orders of magnitude higher than the equivalent CPU code. Applications are shown for simulating the paths of lava flows during volcano eruptions. Both static problems with purely thermal effects (such as lava lake solidification) and dynamic problems with a complete lava flow were simulated.