Abstract <p>Based on the laws of the hydrodynamic flow around a solid body, including a rotating one, some ideas about the shear-inertial mechanisms of propagation and motion of deep convective clouds in a shear atmosphere are developed. The analysis of the wind hodograph in a Lagrangian coordinate system moving along the steering flow reveals the flows dynamically influencing a cloud at different levels, primarily at the surface and middle ones. These flows onto and around an object, together the rear inertial streamline flow of a cloud intensively gaining mass and the rotation of this cloud, form the above mechanisms. When the dynamic flow of the middle layer streamlines the dense body of a cloud in a certain range of values of the Reynolds number, the cloud may enter the vortex stage. This stage may be represented by either stationary cyclonic or anticyclonic vortices, or by their couplet capable of dividing, with a specific mechanism of propagation and motion. Together with similarly appearing surface layer vortices, their total number in a cloud can reach four. A four-vortex complex may contain five stationary updraft zones. The control parameter of the vortex composition of a cloud is the angle of the deviation of the vector of the incoming dynamic flow relative to the perpendicular to the elongation of the dense body of the cloud.</p>