By means of the gravity models reflecting a rheological states of geological environments 3D distribution of density contrast in the heads of six plumes (Yellowstone, Emeishan, Indigiro-Kolyma, Sea of Okhotsk, Indigiro-Kolyma, and Maya-Selemdzha) up to the depth of 200 km are studied and compared with all geological-geophysical data. According to the obtained data, astenospheric parts of plumes have mushroom-like shape, and astenosperic magmas spread under the lithosphere bottom and more rare ‒ under the crust bottom. At the distance of 250‒300 km from central trunks of plumes they are narrowed to diameter of 200–300 km at a depth of 100‒120 km. In heads of the majority of plumes astenospheric magmas merge with the subcrustal viscous layer and approach the Earth’s surface to 40‒50 km. In the majority of the considered plumes their lithospheric and crustal fragments are curved towards the Earth’s surface, In the upper crust layers upwards are sometimes complicated by local downwards (Yellowstone and May-Selemdzha plumes) that is explained by sagging of the dome roofs over the magmatic chambers into subcrustal viscous layer and in asthenosphere. Plumes are often accompanied by zones of the lithosphere stretching (rifts) therefore in the lower lithospheric and crustal sections of plumes linear zones of the lowered viscosity are mapped. The structural position of considered plumes is controlled by borders of lithospheric plates and large segments of the second rank. Identical geometry and rheology of plumes created at different times (Triassic‒Neogene) in the regions which are far removed from each other (the North East Russia, North West of the USA, Southern China, Sea of Okhotsk) demonstrate universality of the tectonic situations promoting penetration of mantle streams into upper layers of the Earth. The main of them are the lithosphere stretching zones, in particular ‒ sites of crossing of multidirectional fractures of a lithosphere and crust.