In supernovae (SNe), where the light curves show evidence of strong and early interaction between the ejecta and the circumstellar matter (CSM), the formation of new dust is estimated to take place in a dense shell of gas between the forward shock (FS) and the reverse shock (RS). For the first time, in this study the mechanism of dust formation in this dense shell is modeled. A set of nine cases, considering variations of the ejecta mass and the pre-explosion mass-loss rates, is considered, accounting for the diverse nature of interactions reported in such SNe. For a single main-sequence mass, the variation of ejecta mass was manifested as a variation of the H-shell mass of the star, lost due to pre-explosion mass loss. We find that the dust masses in the dense shell range between 10(-3) and 0.8 M (circle dot), composed of O-rich and C-rich grains, whose relative proportions are determined by the nature of interaction. Dust formation in the post-shock gas is characterized by a gradual production rate, mostly ranging from 10(-6) to 10(-3) M (circle dot) day(-1), which may continue for a decade, post-explosion. A higher mass-loss rate leads to a larger mass of dust, while a smaller ejecta mass (smaller leftover H shell) increases the efficiency of dust production in such SNe. Dust formed behind the RS, as in our calculations, is not subject to destruction by either the FS or RS and is thus likely to survive in a larger proportion than dust formed in the ejecta.