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A theoretical model of convection in a thick horizontal cloudy layer with free upper and lower boundaries is built up. The cloud layer is supposed to be subjected to the Coriolis force due to the cloud rotation. Such conditions are typical for tornados formation, one of the most dangerous atmospheric phenomena. It is obtained that convection in such a system can look as just one rotating sell in contrast to the usual many sells Benard convection. The tornado type vortices are typical formations different from spatially periodic convective cells because they disappear with distance from the vortex axis. The lower boundary at this convection can substantially go out of the initially horizontal cloud layer forming a single vertical vortex with intense upward and downward flows. The dense air of the lower atmosphere layers is pushed into the upper layers where it is fixed by the radar equipment against a more rare air background.