Some capillary phenomena, shapes of surfaces and menisci of liquids, wetting processes under lowered or zero value of earth gravitation acceleration (weightlessness) are studied. Theoretically, on the basis of computer integration of classic capillarity equations using pre­viously created programs and varying acceleration g values, and experimentally, modelling weightlessness on the Earth (using small volumes, namely drops of a liquid under lowered gravitation action, or creating interphase boundaries between nonmiscible liquids of equal density), the shape of liquid phases surface (for molten metals) are studied in most typical systems: a drop on a solid surface and liquid meniscus in a cylindrical channel. The experiments concerning to wetting contact angles dependence on gravitation discussed today were carried out (independence of wetting contact angle on value and direction of gravitation vector action is shown). The wetting contact angles in model systems are specially measured also at zero gravitational pressure, which is of basic importance for the theory of capillarity. The results are used in technology of materials brazing, powder metallurgy, in manufacturing of heat pipes porous capillary structures with an eye to implementation of these technologies in space environments (microgravitation).