The theory of bubble behavior around an inclusion as a source of gas in liquid metal under the influence of capillary, hydrodynamic and diffusion effects is developed. It is shown that diffusion of the gascomponent in molten metal slows down growth of microcavities.Keywords: inclusion, gas source, bubble, foam metal, foam material, gas-filled cavity, gas diffusion from a bubble, change in bubble radius kinetics, capillarity criterion.A significant part of the research and technical solutions devoted to creating foam metals (or more broadly foam materials) is connected with the pore occurrence and dynamics of pore growth around particles that release gas [1][2][3][4]. Many aspects of known and developing technologies for foam metals relate to the field bounded by powder metallurgy (for example liquid-phase sintering), casting production and chemical heat treatment. At the basis of technology for preparing foam metals there are hydrodynamic, thermal, capillary, and diffusion processes. Analysis of these basic phenomena, each individually or in combination, is extremely important for creating technology because the results of this analysis will make it possible to control a production process as integrating the basic processes indicated above.In constructing a theory for the initial growth of microcavity in molten metal around a particle by the release of gas an attempt has been made to consider hydrodynamic, surface (capillary) and diffusion factors [5,6]. However, in these works it was noted that an expression for the dependence of gas-filled cavity (bubble) radius on time and other parameters of the problem [6, Eq. (19)] adopted as an approximation in theory [5, 6], does not contain the diffusion coefficient for the gas component (diffusant) in the surrounding liquid. Proceeding from general physical considerations it is reasonable to suggest that diffusion should affect bubble growth kinetics. Outflow of diffusant into the liquid surrounding a bubble should reduce gas concentration within the bubble, that in turn should result, according to the Clapeyron-Mendeleev equation, to a reduction in its pressure that is weakening of the "expanding" effect of a gas. In addition, a consequence of gas diffusion from a bubble into the surrounding liquid may be not only a slowdown in its growth, but also compression (so-called withering) and even total dissolution [7]. However, it should also be noted that in [7] factors were considered connected with viscous liquid medium hydrodynamics; the equations derived contained errors that have been considered in [8].In the analysis employed in the current work, as in [5, 6], we shall use a model of a bubble shown in Fig. 1. The aim of the work is to describe mathematically the course of the change in dimensions of a bubble surrounded by some