One of the urgent problems of modern foundation engineering is the selection of reliable beds and foundations for high-rise buildings. This problem is being actively discussed, and, among other things, the Gersevanov Lectures [1] held in 2003 by the Scientific-Research Institute of Foundations and Underground Structures were devoted to it.The "Woolworth Building" in New York, which was constructed in 1913 with a height of 241 m (57 stories) was considered one of the first high-rise buildings. For a long time, the 102-story "Empire State Building" with an overall height of 381 m (448 m with its antenna) was considered to be the world's tallest building. The "World Trade Center" in New York with heights of 415 and 417 m, the "Sears Tower" in Chicago with a height of 442 m, the twin "Petronas Towers" in Kuala Lumpur with a height of 452 m, and the building housing the Taipai Financial Center" in Taiwan with a height of 448 m (508 m with its needle) were constructed later on. It is planned to erect the "World Financial Center" with a height of 492 m in Shanghai, and the "International Business Center" with a height of 580 m in Seoul [2].In "climbing to the heights," designers and builders are encountering the following problems: -evaluation of geologic-engineering and hydrogeologic conditions at the construction site; -determination of vertical loads due to the building, and horizontal aerodynamic loads; -temperature and humidity conditions; -installation and operation of engineering equipment; and, -fireproofing, sanitary-hygienic, and other requirements. Detailed investigation of the geologic-engineering conditions and correct selection of the type of foundations are some of the determining factors.High-rise construction abroad is carried out basically in areas with favorable geologic-engineering conditions: on strong rocky soils, or beds composed of slightly compressible deposits that are not subject to structural transformations.In Frankfurt-am-Main, for example, the geologic-engineering conditions are characterized by a stratum of silty-clayey soils underlain by limestones ranging in depth from 25 to 60 m. The building housing "Commerce Bank I" is constructed on a foundation in the form of a slab 2.4 m thick, which is situated on the clays. Settlements of the building have developed uniformly, and at the moment of stabilization, their maximum value was 22 cm.It is proposed to use foundations with anchors for the construction of high-rise buildings. Friction piles rigidly fixed to a monolithic reinforced-concrete slab are used as anchors. A 70-story 210-m-high building is analyzed for different types of foundations. Settlements and tilts based on mathematical modeling are compared with reliable values established by the Construction Rules and Regulations.