Abstract <p>A diffusion model of dissolution of gas-filled spherical pores in a solid during hot isostatic pressing (HIP) is proposed. It is assumed that the pore surface emits vacancies when a solid is loaded with external pressure, as a result of which the pores shrink in size. Two specific cases are considered: pores with a constant amount of insoluble gas and pores with a gas diffusively dissolving in the material surrounding the pore. In the first case, the increasing internal pressure of the gas in the pore first slows down the process of pore contraction and finally stops it completely when the internal pressure of the gas in the pore becomes equal to the sum of the externally applied HIP pressure and the Laplace pressure due to the pore surface tension. In the second case, the internal gas pressure in the pore decreases rapidly due to the dissolution of the gas in the material surrounding the pore and therefore pore contraction does not stop. When the pore reaches a sub-micron size, the pore contraction is quickly accelerated due to the increasing Laplace pressure and finally the pore annihilates.</p>