Stylolites are localized dissolution surfaces commonly found in sedimen- tary rocks. Stylolites have been extensively studied due to their important role in controlling dissolution, precipitation, deformation, and fluid transport in rocks. Field observations indicate that stylolite formation and morphology are strongly correlated both with the surrounding stress and with the distribution of clays within the host rock, yet the mechanism by which they form remains enigmatic. We present results from a newly developed two-dimensional Spring-Network Model that studies stylolite forma- tion by pressure-solution with and without the presence of clays, where clays play a role of enhancing pressure solution. We use our model to test the relative role of stress and clays in controlling the localization of dissolution into stylolites. In contrast to the common paradigm, our results suggest that pressure solution alone, in the absence of catalyzing clays, does not lead to spontaneous localization of dissolution into stylolites. Instead, we propose a new coupled clay-pressure-solution feedback to localize stylo- lites, a coupling that we observe in our model: a region with a slightly larger clay fraction will experience enhanced dissolution, and will thus accumulate more residual clays, which will act to further enhance pressure solution in that region, and accumu- late even more clays. Stress is a necessary component in this feedback as it controls the direction of stylolite propagation, and facilitates lateral propagation.