The presence of dry fluvial river channels and the intense cloud activity in the south pole of Titan over the past few years suggest the presence of methane rain. The nitrogen atmosphere of Titan therefore appears to support a methane meteorological cycle that sculptures the surface and controls its properties. Titan and Earth are the only worlds in the Solar System where rain reaches the surface, although the atmospheric cycles of water and methane are expected to be very different. Here we report three-dimensional dynamical calculations showing that severe methane convective storms accompanied by intense precipitation may occur in Titan under the right environmental conditions. The strongest storms grow when the methane relative humidity in the middle troposphere is above 80 per cent, producing updrafts with maximum velocities of 20 m s(-1), able to reach altitudes of 30 km before dissipating in 5-8 h. Raindrops of 1-5 mm in radius produce precipitation rainfalls on the surface as high as 110 kg m(-2) and are comparable to flash flood events on Earth.